Reverse sham bedspread: MAKE IT YOUR CUSTOM TO ADD FLAIR TO YOUR LAIR

Содержание

MAKE IT YOUR CUSTOM TO ADD FLAIR TO YOUR LAIR

What is it about custom-made bedspreads that makes them so much more attractive (and expensive) than the ready-made variety?

The answer lies in the wider variety of fabrics available. As in any custom-made article, uniqueness is the main attraction.

Coordination with other fabrics and/or wallpapers in the room is the other big enticement.

If you can conceive it, someone can make it. And you don`t have to create a masterpiece to get an attractive, room-enhancing spread.

Here are some styles that any good bedspread-maker should be capable of producing for you:

– The reverse sham: Think of how you usually make your bed. You take the spread, cover the bed, fold back the top, put pillows in place, then fold the spread over the pillows so the edge of the spread faces the headboard.

With the reverse sham, you do the same first two steps; before folding back, you stick the pillows in, then fold the spread up and over them in the reverse direction so the edge of the spread faces the base of the bed.

So what`s the big deal? Some find this an easier way to make the bed.With the reverse sham, you have the option of tucking or not tucking. A decorative welt can be added to the edge so you do not tuck. Another idea is to use a different fabric on the reverse part to add contrast.

– Fitted spread with perimeter welt and contrasting gusset: A fitted bedspread takes the guesswork out of making the bed. You know right where the spread should go without having one side drape lower than the other side.

In the corners you have the option of adding a gusset, which is the inside of the pleat. This gusset can be made with an accent color, giving the spread extra appeal.

– Shirred drop with perimeter welt: This one is quite feminine. The drop is shirred while the top remains flat. The separation is treated with a welt that can be as thin or as fat as you like.

The welt separation also gives you an opportunity to switch fabrics; with one fabric on the top of the bed and another for the shirred drops. If it`s coordinated right, you can use a third faric on the welting.

– Throw with jumbo welt at the bottom: You can take a common throw spread and perk it up by adding a jumbo welt to the bottom. Here again, the welt can be a complementary fabric.

– Throw with jumbo welt at perimeter: This is the same as above, only the welt frames the mattress rather than the bottom of the spread.

With the welt around the perimeter of the mattress, you have the same convenience as the fitted style in that the guesswork is taken out of making the bed. You know just where the spread should go without having to run back and forth from one side of the bed to the other. If you have a king-size bed, you know how tiring that can be. Be creative with this welt. Try a knot on the corners.

Quilted Bedspreads-Australia,NSW,VIC,QLD,Melbourne,Sydney,Brisbane|Quilts & Bedspreads-Romeo Imports



Anastacia




This stunning floral design is printed on luxurious jacquard fabric . .


AU$310.00
Ex Tax: AU$310.00


ARABELLA QUEEN SIZE BEDSPREAD BY BIANCA

IVORY BOUDOIR BEDSPREAD.

STUNNING JACQUARD DIAMON..


AU$399.00
Ex Tax: AU$399.00


Ashton Bedspread Set Black  (By Bianca)

Provincial black floral motifs are beautifully c..


AU$230.00
Ex Tax: AU$230.00


Ashton Bedspread Set Black

Provincial black floral motifs are beautifully contrasted on a cri..


AU$220. 00
Ex Tax: AU$220.00


BEDSPREAD SET SANTORINI BLUE/TAUPE STRIPED QUEEN SIZE QUILTED

SANTORINI  BEDSPREAD SET&n..


AU$300.00
Ex Tax: AU$300.00


BELLE ECRU QUEEN SIZE BEDSPREAD SET (BY BIANCA)

Belle is an exquisite Provincial style bedspr..


AU$245.00
Ex Tax: AU$245.00


NOTTINGHAM BEDSPREA D  (BY BIANCA)

This splendid Italian fabric depicts a fine jacquard,..


AU$300.00
Ex Tax: AU$300.00


BARKLEY    (BY BIANCA)

 100%cotton filled Throwover type Bedspread with a. .


AU$259.95 AU$219.00

Ex Tax: AU$219.00


TUSCANY BEDSPREAD  (BY BIANCA)    GOLD COLOUR


 

DOUBLE BED BEDS..


AU$350.00 AU$290.00

Ex Tax: AU$290.00


DUCHESS BEDSPREAD

THIS EQUISITE BEDSPREAD IS MADE FROM ONE OF THE

FINEST WOVEN FABRICS AV..


AU$500.00
Ex Tax: AU$500.00


CREAM QUEEN SIZE SMITHFIELD BEDSPREAD SET

Smithfield Bedspread Set Charcoal

Instantly cre..


AU$150. 00
Ex Tax: AU$150.00


Eleanor Bedspread Silver

Eleanor brings elegance to the classic throw over style bedspread. G..


AU$400.00
Ex Tax: AU$400.00


FLORENCE BEDSPREAD  (BY BIANCA)

THIS BEDSPREAD IS INSPIRED BY A FRENCH PROVINCIAL BOUDOI..


AU$160.00
Ex Tax: AU$160.00


FLORENCE QUEENSIZE BEDSPREAD SET  (BY BIANCA)  .

This bedspread is inspired by a fr..


AU$230.00
Ex Tax: AU$230.00


GABRIELLE QUILTED BEDSPREAD

MUSHROOM COLOUR 

AUSTRALIAN MADE

STANDARD QUEEN SIZE. .


AU$375.00
Ex Tax: AU$375.00


Hayes Bedspread Set Soft Blue (By Bianca)

Come home to a beautiful and relaxed atmosphere wit..


AU$300.00
Ex Tax: AU$300.00


Illiana bedspread set stone – Also available in stone

Features an intricate embroidered desig..


AU$149.00
Ex Tax: AU$149.00


Madeline Burgundy Bedspread  (by Bianca)

Stunning floral posies flow beautifully on this..


AU$279. 00
Ex Tax: AU$279.00


Madison Bedspread Set White

Madison brings contemporary lux to a classic bedspread. The intri..


AU$320.00
Ex Tax: AU$320.00


ROSEDALE FLORAL  QUEEN SIZE BEDSPREAD  (BY BIANCA)

Incorporate timeless heritage co..


AU$199.95
Ex Tax: AU$199.95



Shayla (BY BIANCA)




A beautiful bedspread intricately embroidered with a classi..


AU$399.00
Ex Tax: AU$399. 00


Shimmer Bedspread Set

Faux Silk and Flocked

Available Midnight Black 

 
..


AU$250.00
Ex Tax: AU$250.00


SHIMMER BEDSPREAD SET

Faux Silk and Flocked

Queen Size  Available In  Midnight ..


AU$250.00
Ex Tax: AU$250.00


TARANA BEDSPREAD SET 

3 PIECE QUEEN SIZE  BEDSPREAD SET 

A luxurious jacqu..


AU$450.00
Ex Tax: AU$450.00


Terika Grey Queen Size Bedspread by Bianca

Transfer the relaxed feel of autumn into the bedro. .


AU$199.95
Ex Tax: AU$199.95


 

Abselutely gorgeous Vintage designed Chenille ice cake Bedspread

Thick and plush w..


AU$400.00
Ex Tax: AU$400.00


 

Abselutely gorgeous Vintage designed Chenille ice cake Bedspread

Thick and plush w..


AU$400.00
Ex Tax: AU$400.00


Abselutely gorgeous Vintage designed Chenille ice cake Bedspread

Thick and plush with wide li..


AU$550. 00
Ex Tax: AU$550.00

Norbar Fabrics









































WHOLESALE PRICE LIST

EFFECTIVE JAN. 2012

General Information:

1.All orders or changes must be submitted in writing.

2.Norbar Fabrics will not be responsible for any oral orders or changes.

3.TERMS: No C.O.D.’s!!!

4.Net 30 accounts ship F.O.B. from Norbar Fabrics.

5.Major credit cards accepted: AMEX, MasterCard, VISA, Discover.

6.No cancellations on custom bedding orders.

7.No C. O.M.!!!

8.All prices, terms & specifications are subject to change without notice

TWIN LINE QUILTING:
AVAILABLE ON ALL QUILTED PRODUCTS EXCEPT COMFORTERS.

Available in white nylon thread only!

White poly/cotton lining only!

Monofilament thread no longer available, self color thread not available.

Please specify polyester fiberfill – 4oz. or 6oz. (6 oz. Standard).

Fabric for Bedspreads and Coverlets are machine quilted first, then seamed.

Serged seams will be present on the back.

Only fabrics up to 58” wide can be Twin Line Quilted.

Not suitable for pre-seamed or irregular sized pieces.

  FRAME QUILTING:
AVAILABLE ON ALL QUILTED PRODUCTS EXCEPT COMFORTERS.
● Self color, matching thread is used.

● Please specify polyester fiberfill – 4, 6, 8 or 10 oz. (10 oz. Standard).

● White (Standard) or Ivory poly/cotton lining available, please specify.

● Throw Style Reversible Spreads available w/self-welt.

● Fabric is seamed before quilting when making Bedspreads and Coverlets.

● Custom pattern sizes require additional set-up cost.

● Additional charge to align & hide seams with quilting on solid fabrics.
   
  FRAME QUILTING STYLES:
 
   
  CUSTOM BEDSPREADS & COVERLETS:
Price includes Labor, Quilting & Lining.

Suggested yardage based on 54” solid goods, additional yardage for pattern repeats.
 
 
 
 
   
  BEDSPREAD & COVERLET OPTIONS:
  STRAIGHT DROP:

TO ALL SIZES ADD

WELT ( ¼”, ½” OR STANDARD ¾”)

SHIRRED WELT (½” OR STANDARD ¼”)

RUFFLE (SPECIFY SIZE)

PLEATED RUFFLE (SPECIFY SIZE)
YARDAGE

1 YARD

2 ½ YARDS

3 YARDS

4 YARDS
     
  SCALLOPED DROP:

TO ALL SIZES ADD

WELT ( ¼”, ½” OR STANDARD ¾”)

SHIRRED WELT (½” OR STANDARD ¼”)

RUFFLE (SPECIFY SIZE)PLEATED RUFFLE (SPECIFY SIZE)
YARDAGE

1 ½ YARDS

2 ½ YARDS

3 ½ YARDS

4 ½ YARDS
   
 
ADDITIONAL LABOR SERVICES AVAILABLE:
ALIGN CHANNEL OR SQUARE QUILTING TO HIDE SEAMS (SOLIDS ONLY) REVERSE SHAM (ADDITIONAL YARDAGE REQUIRED)

BANDING (USING 54” FABRIC)

CUSTOM SCALLOP (IF NOT OUR STANDARD SCALLOP) ROUND OR SHAPED BEDSPREADS (I. E. BOAT MATTRESS) VELVET, CHENILLE, SUEDE, MATELISSE OR UPHOLSTERY WEIGHT FABRICS DOUBLE-SIDED FRAME QUILTED THROW STYLE, FOR REVERSE WELTING DROPS OVER 21”, SEE LABOR NEXT SIZE LARGER, KING SIZE ADD 20% FLANNEL INTERLINING

PREQUILTED, VINYL, UPHOLSTERY WEIGHT OR NAP FABRICS – ADD 15%

Please note for COM lining:

Fitted Bedspreads are NOT reversible nor can be turned back at the head to show the lining. There will be very unsightly seams where the quilting is cut apart to insert the welt between the mattress top and the drops.

 
   
  COMFORTER QUILT DESIGNS:
(DUAL-SIDED, REVERSIBLE)
 
 
  OPTIONS:

Variation from standard sizes: ADD 25%

½” Welt or Cord (4 Sides).

½” Flat Welt (4 sides).

Ruffle (3”) – Adds 3” all around standard size comforter.

Round Corners (2).

Seam Alignment w/Channel or Square Quilt.

Color matched or contrast thread.
20 oz. standard polyester fiberfill.

4 oz., 6 oz., 8 oz., or 10 oz. Polyfill also available for lighter weight & lower loft.
   
  DELUXE DUST RUFFLES:
Self Fabric Framing Top of Platform.

Drops up to 15” (over 15” add 20%).

4 sided drops add 20%.
 
   
  PILLOW SHAMS:
Finished with Zipper on Back at bottom.

Options may require additional yardage.

Approximate yardage shown.
 
  OPTIONS:
   
  DUVET COVERS
  Standard Sizes & Yardage Requirements

Unquilted is Standard, Twin-Line or Frame Quilted also available.

Standard ¼” Welt on 4 sides, other size welting available.

Matching cotton thread, no visible stitching.

Velcro or Zipper closure, please specify.

Head, Foot or Side closure available, please specify.

Available lined, please call for pricing.

Yardage based on 54” solid.

Please specify exact Comforter measurements if not standard size.

 
   
   

Bianca Reverse Sham Bedspread Collection in All Sizes Quilts, Bedspreads & Coverlets Home & Garden worldenergy.

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Bianca Reverse Sham Bedspread Collection in All Sizes Quilts, Bedspreads & Coverlets Home & Garden worldenergy.ae

Bianca Reverse Sham Bedspread Collection in All Sizes,Bianca Reverse Sham Bedspread Collection in All Sizes,King Bedspread: 293 x 260cm,Single Bedspread: 91 x 188 x 55cm,King Single Bedspread: 110 x 203 x 55cm,Double Bedspread: 137 x 188 x 55cm,Queen Bedspread: 152 x 203 x 55cm,King Bedspread: 183 x 203 x 55cm, Single Bedspread: 202 x 249cm,King Single Bedspread: 220 x 260cm,Double Bedspread: 250 x 249cm,Queen Bedspread: 264 x 260cm.Sham Bedspread Collection in All Sizes Bianca Reverse.

  1. Home
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  4. Quilts, Bedspreads & Coverlets
  5. Bianca Reverse Sham Bedspread Collection in All Sizes

Bianca Reverse Sham Bedspread Collection in All Sizes

Bianca Reverse Sham Bedspread Collection in All Sizes

Bianca Reverse Sham Bedspread Collection in All Sizes. Single Bedspread: 91 x 188 x 55cm,King Single Bedspread: 110 x 203 x 55cm,Double Bedspread: 137 x 188 x 55cm,Queen Bedspread: 152 x 203 x 55cm,King Bedspread: 183 x 203 x 55cm. Single Bedspread: 202 x 249cm,King Single Bedspread: 220 x 260cm,Double Bedspread: 250 x 249cm,Queen Bedspread: 264 x 260cm,King Bedspread: 293 x 260cm.. Condition:: New with tags: A brand-new, unused, and unworn item (including handmade items) in the original packaging (such as the original box or bag) and/or with the original tags attached. See all condition definitions : MPN: : Does Not Apply , Brand: : Bianca: Material: : Polyester , Type: : Bedspread .

OUR VALUES

TO CREATE VALUE AND MAKE A DIFFERENCE
INTEGRITY

We believe in integrity and transparency in all areas of our business so as to ensure customer confidence in our ability to meet and exceed international industry standards.

INNOVATION

To bring inspiration and innovation into business through advance technologies and processes from leading industries around the world, in order to support our customers with best available technology to meet their demand.

PARTNERSHIPS

Our strength is focused on forging reliable partnerships that further our capability to build healthy relationships with our clients.

COMMITMENT

Our commitment to our promises is highlighted by our pursuit of complete customer satisfaction, on-time performance and responsive support throughout.

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our vision is to thrive as a business over the years and beyond, looking ahead, understand the trends and forces that shape our business in the future and move swiftly to prepare for what is to come. It creates a long-term destination for our business and provides us with a roadmap for winning together with our valued partners and clients.

Mission

Our Road Map Starts With Our mission which is enduring. It declares our purpose as a company and serves as the standard against which we weigh our actions and decisions.

  • To provide state of the art, well proven, quality products and services using top notch innovation and expertise
  • To develop and maintain long term relationships with satisfied clients and suppliers
  • To create safe, challenging, and enjoyable work environment where employees share in corporate growth and success.

Bianca Reverse Sham Bedspread Collection in All Sizes


Bianca Reverse Sham Bedspread Collection in All Sizes, Bianca Reverse Sham Bedspread Collection in All Sizes

Print Quilted Bedspread Back To Sherp Reverse Cold Weather Bedding Collection Suppliers,Print Quilted Bedspread Back To Sherp Reverse Cold Weather Bedding Collection Manufacturers


Printed Quilts Sherpa Comforter Bedding Set


This plush comforter is ideal for colder months and can even be used as a cozy addition to your bedding! It includes an extra layer of faux sherpa for ultra-softness.   Lined in a cozy sherpa, it turns an ordinary room into a welcome sanctuary!


Features:


  • Front: flannel fabric 220gsm, Reverse: sherpa fabric, 200gsm

  • Set includes 1 quilt and 2 shams (1 sham for the twin size)

  • Ultra-soft for sweet dream with less tossing and turning

  • Water wash with soft cozy feeling

  • Prewashed and preshrunk for immediate use and to ensure soft touch for cozy hand feel

  • Pinsonic embossed for this quilt 

  • 100% polyester filling, 120gsm

  • Straight edge with self fabric piping

  • Available in various colors and sizes

  • Easy care machine washable, wash in cold water and gently cycle, tumble dry in low temperature


Bedding Dimensions

Twin Dimensions:
Quilt: 68 inches wide x 86 inches long
Sham: 20 inches wide x 26 inches long
Full/ Queen Dimensions:
Quilt: 92 inches wide x 92 inches long
Shams: 20 inches wide x 26 inches long
KING Dimensions:
Quilt: 106 inches wide x 92 inches long


Shams: 20 inches wide x 36 inches long

Single:   160×220+1x50x70cm


Double:  220×240+2x50x70cm


Queen:   240×260+2x50x70cm


King:      260×280+2x50x70cm





Handcrafted Quilts & Coverlets | The Company Store

Accent Your Bed with Quilts, Coverlets & Bedspreads

Our extraordinary handcrafted quilts, bedding, coverlets, and bedspreads are one-of-a-kind works of art, each one a beautiful way to infuse your room with pattern, color, and sumptuous texture. We have quilts and coverlets for beds in twin, full, queen, and king sizes—and matching shams complete the bed, creating a coordinated look you’ll love. Find quilts for men, women, teens, and kids. Quilts and coverlets are lightweight enough to use during summer months, and they layer wonderfully for extra warmth in winter. Like a coverlet, bedspreads are a decorative top layer that adds a bit of warmth.

Our cotton coverlets, quilts, and bedspreads put traditional handcraftsmanship on display. Our collection includes an ever-changing selection of solid and matelassé coverlets. From bright florals and timeless stripes to bold geometrics and global-chic woodblock prints, there’s something to complement every style. Find quilts, bedspreads, and coverlet bedding sets with beautifully finished traditional or embroidered details. Our matelassé coverlets add texture and subtle sophistication to the bed. Supremely soft and intricately patterned, matelassé bedding is a luxurious staple for all four seasons. For another year-round bedding essential, try our soft, lightweight Company Quilt—it comes in over a dozen colors—or explore our quilt, bedspread, or coverlet sets with matching shams.

Quilts & Coverlets FAQ

Is a Quilt a Blanket?

A quilt is a type of bed covering that is constructed with three parts: Two outside pieces are stitched, or quilted, to form the top and bottom layers that surround an inside layer of batting. A blanket is usually a single layer that is not quilted.

Is a Coverlet a Blanket?

A coverlet is a lightweight blanket used for decoration or to add warmth. It is often the topmost bedding layer but may be layered beneath a quilt or comforter for extra warmth during cold months.

Is a Coverlet the Same as a Bedspread?

Coverlets and bedspreads are similar styles of bedding: They are both decorative, single-layer bed coverings that provide warmth.

What’s the Difference Between a Bedspread and a Coverlet?

A coverlet tends to be slightly smaller than a bedspread: Coverlets usually reach the bottom of the box spring or mattress, while bedspreads drape nearly to the floor.

What’s the Difference Between a Coverlet and a Quilt?

A coverlet is a single-layer bedding piece, while a quilt consists of a top and bottom fabric layer stitched around a warm layer of batting.

What’s the Difference Between a Coverlet and a Comforter?

A coverlet is a lightweight blanket without fill, while a comforter or duvet insert is a shell filled with down or down alternative for a warmer, lofty bedding piece.

Sleepwell Mattresses

  • How is the Cocoon Mattress unique?

    All mattress in India come with the same feel for both partners. However, each partner may like a different feel for a comfortable and healthy sleep. One partner may prefer a soft feel while the other may prefer a firm one.
    Cocoon is a first of its kind mattress which comes with Dual Feel in the top layers – Gentle & Firm. Depending on the personal preference of each partner, you can interchange these layers to get the preferred feel for each of you on the same mattress for a comfortable sleep.

  • Gentle or Firm? How do I decide?

    While ordering Cocoon Mattress, you can choose Gentle for extra comfort or Firm for extra support. Gentle feel is suitable if you want a soft and bouncy type of feel for extra comfort. A Firm feel is suitable if you want a slightly hard surface for extra back support. Cocoon Mattress will be delivered to you with choice of feel you selected while ordering.

    So, you can decide between 3 options :
    1) Firm feel on both sides of the bed
    2) Gentle feel on both sides of the bed
    3) One side Firm and other side Gentle

    If you however need to change it, you can flip the layer on each side easily yourself to get your preferred feel.

  • How do I change the feel? From Gentle to Firm or vice versa?

    Each partner can change the feel for him/herself easily on your own. The mattress comes with a zip. So, as per the preference of each partner, you can unzip the mattress top cover and change the top two layers for the desired comfort of each partner.It is convenient and simple!

  • What is Half & Half ?

    Half and Half is a revolutionary product innovation where you can have two different feels on the two sides of the same mattress – Gentle & Firm. So, as per you and your partner’s need, each side of the bed can be customised within the given feel options. You can also have gentle feel for both of you or firm feel.

  • How does this Half & Half work in a Cocoon’s single mattress size?

    Half & Half is only available in double size mattress. In a single size mattress, you get an option of Dual Feel. So, as per your preference, you can unzip the mattress top cover and flip the top two layers for your desired comfort – firm or gentle. It is convenient and simple!

  • What is Mattress in a Box?

    The terms “mattress in a box” or “bed in a box” refer to a mattress that is compressed and placed in a box for shipping. The mattress is compressed using a special press machine, vacuum packed in plastic, and rolled into a cylindrical shape. This process – also known as “roll packing” – reduces the mattress to a much more compact size, allowing it to fit in a box that can be shipped via standard delivery. These mattresses are comparable to models sold in Offline stores in terms of construction and performance.

  • How will the Cocoon be delivered?

    Cocoon mattress is compressed using a special machine, vacuum packed in plastic, and rolled into a cylindrical shape,allowing it to fit in a box that is shipped to you. The mattress will come with your choice of feel at the top that you select while ordering.

  • Is it available in retail market?

    Yes. It is available for sale at our Exclusive Brand Outlets. You can go there and make a purchase. However, as Cocoon is a Mattress in a Box, it is shipped directly from the company to you.

  • Is it available on Amazon or Flipkart?

    It will be available on Amazon and Flipkart soon. However, 30 Day Free trial will not be available on Cocoon mattress sold through marketplaces.

  • Can the Cocoon mattress get damaged when it’s compressed for shipping?

    A common misconception among consumers is that roll packing causes permanent damage to the mattress. However, mattresses in a box are designed to be highly resilient. Once the plastic wrapping is removed, the layers will expand until the Cocoon mattress reaches its full intended shape.

  • What is DIY?

    DIY is Do It Yourself. You can customise your mattress easily on your own. The mattress comes with a zip. So, as per your preference, you can unzip the mattress and interchange the top two layers for your desired comfort need. It is convenient and simple!

  • How can I Return Cocoon Mattress under 30 Day Free Trial ?

    – Your trial begins after your order is delivered.
    – Return Request can be raised at www.mysleepwell.com.
    – We will arrange reverse pickup for the mattress and this will be entirely free.
    – We will process a full refund once we receive back the mattress at our facility.
    – Refunds will be credited in the form of your original payment method.
    – In case of COD Order, our customer care team will contact you to process your refund.

  • How can I opt for No Cost EMI ?

    – Add products to your cart.
    – Click on ‘No Cost EMI’ when you proceed to pay.
    – Choose your applicable No Cost EMI plan.
    – Make the payment via credit card from any partnered bank.
    – At the time of purchase, a chargeable interest amount will be provided to you as an upfront discount, effectively giving you the benefits of a No Cost EMI!

  • Football for two – Ogonyok No. 2 (5355) dated 19.01.2015

    No matter how hard the FIFA functionaries tried to aggravate the struggle for the Ballon d’Or, hinting that they could hand it over to goalkeeper Neuer, the prize was again played by forwards Messi and Ronaldo. As a result, the latter accepted the congratulations. Why did the presentation of one of the main football awards become a dispute between two geeks?

    Sergei Pankratov, Barcelona

    At the end of December 2014, in the Portuguese city of Funchal on the island of Madeira, excitement reigned – they were waiting for the football megastar Cristiano Ronaldo with his son.There was a reason to visit their native land: fellow countrymen, without waiting for the court of sports history, decided to erect a monument to the most famous resident of the city during his lifetime.

    Sculpted forward by local sculptor Riccardo Veloza. When the four-year-old Ronaldo Jr. pulled off the white coverlet from the statue, Cristiano himself, like many of those present, froze in slight bewilderment. The crowd of inhabitants of Funchal was looking at a dumpy man, neither in face nor figure and not close to resembling the original standing next to him. But the sculptor very vividly emphasized the manhood of Ronaldo, and this suggested that the sculptor took as a sample posters on which Cristiano advertised underwear from Armani.

    The Internet exploded with enchanting comments, the most popular of which was: “The bulge of the statue of Ronaldo is greater than the statue of Messi itself.” The fact is that the monument erected to the Argentine striker last summer in Buenos Aires is really modest. If the height of a bronze ronaldo is 3 meters 40 centimeters, then the Messi monument is larger than a wax figure from Madame Tussaud’s.

    But in the end, Barcelona accepted the sculptural challenge: the president of the Catalan club promised that a worthy monument to Messi would be erected in the new stadium in three years.It is known that the leadership of Barça wants to build the largest stadium in the world. Apparently, there will be a monument to match.

    Two worlds, two idols

    Two great footballers of our time play catch-up in literally everything. No sooner had Messi knocked out a contract for the highest paid football player (42 million euros per year, including bonuses), as Ronaldo began to hint to the management of Real Madrid that he would leave the team if he did not achieve better conditions. And he did! Now, taking into account bonuses, he receives 49 million.As soon as the Portuguese moved into a luxury villa for 10 million euros, the leader of Barcelona began construction at a cost of 12 million. Ronaldo got a son, and a year and a half later, Messi had a son. But if the birth of the heir to Cristiano is shrouded in mystery (either a baby from a “test tube”, or from a waitress from the United States), then the mother of Messi’s child is known, this is his common-law wife Antonella Rocuzzo.

    Leo was so happy about the appearance of his son that he even got a tattoo in honor of little Thiago. Guess where? Of course, on the most precious and beloved left! So he ordered the artist to have their little hands hugged daddy’s shock leg on the tattoo.

    But the most fundamental rivalry between Ronaldo and Messi is in the fight for the main football award, the FIFA Ballon d’Or. Leo already has four statuettes of the best football player in the world, Cristiano, before the last ceremony in Zurich, had two. As the knowledgeable people say, passions, surrounded by two football titans, ran high to the limit. After all, if Messi was recognized as the best player of 2014, Ronaldo would hardly have been able to catch up and even more so to surpass the achievement of the Argentine!

    As a result, any story about Ronaldo will not be complete if there is no comparison with Messi.This rule applies, however, in the opposite direction.

    Ronaldo and Messi are not just different, they are complete opposites. Ronaldo is a stately conqueror of women’s hearts, with all his appearance radiates power and confidence. And Messi is miniature, not inclined to narcissism, does not like noisy displays of emotions. This is very noticeable at social events, where Cristiano immediately attracts attention. Lionel, on the other hand, tries to avoid being noticed.

    There is a version that these differences come from childhood.Ronaldo, for example, from an early age is convinced of his own exclusivity, which is not the merit of his mother-cook and father-gardener, who, in addition to Cristiano, raised his older brother and two sisters (his father also liked to stay in the pub and often came drunk). In a word, young Ronaldo nurtured his ambitions himself, as well as a painful attitude towards criticism. It is known that at the age of 14 he even threw a chair at the teacher, for which he was expelled from school. Ronaldo’s mother, out of sin, decided to send the irrepressible teenager to a football school.There, his ascent to the stars began: as a teenager, Ronaldo began to play for an adult club.

    Messi’s childhood was different. He also came from a simple family: his father was a metallurgist, his mother was a cleaner, and there were also four children in the family. But, unlike Cristiano, Leo was always docile, adored his grandmother, and in his first interview he called his older brother Rodrigo, who then played in the amateur team of his native Rosario, the best football player in the world.

    However, his peaceful character did not prevent little Lionel from performing miracles on the field, which quickly brought him from the provincial Grandolini to the capital’s Grand River Plate.At the same time, the genius boy started all his debut matches in new clubs with at least a hat-trick!

    One problem haunted his parents: he stopped growing. Hence the nickname Bloch, to which they soon began to respectfully add – Reactive. It soon became clear: for growth, expensive hormonal injections are needed, there was no money for them in the family.

    But a lucky man, as they say, will win with a tram ticket. Lionel’s father, Jorge, decided that the last chance for his son’s treatment was to get to Barcelona, ​​where he sent him to Barcelona for viewing.Money for a ticket to Spain was collected from friends. But Jorge guessed right: the Barça coaches were impressed by Lionel’s abilities, he was enrolled in the club, of course, taking upon himself all the costs of treatment. On October 30, 2000, 13-year-old Leo became a Barça youth player and scored five goals in his first match.

    The Portuguese also entered Real Madrid on a white horse: he just received the first FIFA Ballon d’Or for playing at Manchester United and did not see any competitors in the Pyrenees.

    Why did Cristiano leave Manchester, where he was already the leader, and the legendary Sir Alex Furguson begged him to stay, the answer is simple: Ronaldo is Portuguese.Every budding Portuguese teenager in football sleeps and sees himself not in Benfica and Porto, but in Real Madrid or Barcelona. As Ronaldo himself said, “I moved to Real Madrid to become one of the best, and maybe the best player in the history of the royal club.”

    Everything went to the fact that he would achieve his goal. If not for the appearance of this Jet Flea Messi, who has long been in the shadow of the previous leader of Barcelona – Ronaldinho. But as soon as the Brazilian left the Catalan club, Messi “exploded” – every match, a hat-trick.It seemed that Leo would “take away” all the records and titles of the Spanish Example and the Champions League, which Ronaldo tried on.

    As a result, instead of taking the throne, Ronaldo received an eternal race for the leader. Of course, this increases motivation: last year, for example, in the fight for the Ballon d’Or, Ronaldo and Messi rewrote a cloud of football records. But another thing is also obvious: the long-term rivalry of athletes easily turns into hostility, especially if it is heated up by the press. For journalists, this is intrigue, exclusive.For “Real” and “Barcelona” additional income, because on the “reality show” Ronaldo versus Messi tickets are sold like hot cakes. However, few people think about what it is like to be a participant in this “performance”.

    Off-ball games

    Just a month ago, a scandal broke out in the Spanish press. The famous journalist Guillem Balagu published excerpts from the new book, where, among other things, he said that Ronaldo invented the nickname cabronazo (“bastard”) for Messi. And that he calls so even his partners in “Real”, if they suddenly allow themselves a kind word about the Argentine…

    I will not reveal a secret: Messi is not liked in “Real”. It would be surprising if this were not the case. Barça are the main rival, and their leader is the main irritant for the players of the royal club. And therefore, as another Spanish journalist writes, Diego Torres, if “Real” loses to the Catalans, surrounded by Ronaldo is not called a “flea” and “dwarf” Messi.

    However, the retinue of the Barcelona Argentinean responds the same way. For example, Leo’s older brothers can easily post on the Web a photo that is not very pleasant for Ronaldo or leave an evil comment about him.The journalist, who visited Rosario, Messi’s hometown, talked with his older brothers – Rodrigo and Matias. The conversation went lightly and cheerfully until it turned to Ronaldo. The brothers instantly forgot about etiquette: “This name is a curse for us, so we won’t even mention it!”

    That the relationship between the two football geniuses is not the easiest can be seen from the results of the voting for the candidates for the Ballon d’Or. Both Messi and Ronaldo, as captains of the national teams of their countries, could write each other’s names on the list of candidates for the prestigious award, but they never did this, although they know each other’s worth very well.

    Another thing is that all this – from the unwillingness to vote for each other to the desire of the retinue to please idols, belittling the opponent – fits into corporate football ethics. While the accusation brought forward by Guillem Balage is not. By the same standards, this is already a “dirty game”.

    Therefore, Ronaldo immediately reacted by posting on Facebook: “There is information circulating in the news that I have come up with an insulting nickname Lionel Messi. This is an absolute lie. My lawyer will take action to bring the liars to justice.I have great respect for all colleagues, and Messi is no exception. “

    To confirm his sincerity, Ronaldo decided on a symbolic gesture. During a recent friendly match between the national teams of Argentina and Portugal in Manchester, before entering the field, he approached Messi and hugged him in a friendly manner. Leo and Cristiano smiled and exchanged a couple of phrases. For the first time (!) In many years that we met on the football field.

    English journalist Pete Jenson, a witness to the episode, is convinced that Ronaldo’s act was sincere.In his opinion, in recent years, Cristiano has generally changed, matured, became wiser. “For years,” writes Jenson, “Messi looked like a shy child prodigy, while Ronaldo was considered a poser. And few people noticed that the image of both players has undergone major changes.”

    Just one stroke. A couple of years ago, Cristiano wanted to buy out Sheikh Hamdan ibn Mohammed ibn Rashid al-Maktoum, who lives in Dubai, who owns one of the general sponsors of Milan, the Emirates Group.The Sheikh was ready to buy a quarter of Milan shares for 500 million euros. And he aimed specifically at Ronaldo, intending to offer 200 million for the Portuguese. Of course, Cristiano’s salary would have reached an astronomical amount.

    Real Madrid have already begun to think about a deal. At stake was a double profit – in 2009, Manchester United were paid 95 million euros. But when asked about the opinion of Cristiano, he did not want to leave: “I dream of winning the Champions League with Real Madrid.” And he really won. As they say, the man said – the man did!

    After that, Ronaldo increasingly began to open up from an unexpected side.Well, who would have thought that this macho, nicknamed the Terminator, was so touching about his son? Well, who would have thought that tears would come to his eyes at the ceremony of presenting him with the long-awaited second Ballon d’Or?

    As the media image of Ronaldo becomes more and more human, Messi, on the contrary, loses this humanity. Take the same story with tax evasion. The humble and quiet Leo turns out to regularly understate his income in his tax return. As a result, over 5 million euros came in.Messi returned the money to the Spanish treasury, but the residue remained. There is also a criminal case, as a result of which Leo may face a real term. This story has clearly tarnished the image of the Barcelona leader.

    In addition, along the way, it turned out that the shy child prodigy over the years turned into a real “locker room dictator.” As the same Guillem Balagu writes in another book, co-authored with ex-Barça coach Josep Guardiola, “the whole game at Barcelona was built around Messi, who was collecting Ballon d’Or.But such a success turned the head of a young and shy Argentinean, in whose behavior arrogance and selfishness began to show more and more clearly. “

    A whole chapter is devoted to Lionel in the book called “Messi the Man-Eater”. It is clear from it that it was because of the Argentine that Zlatan Ibrahimovic, Josep Guardiola himself, and forward David Villa, whom Messi covered with a “three-story” right on the field, when he shot on goal, and did not pass Leo, left Barça. The last season seems to confirm that the Barça leader has bronzed.Following Guardiola, he decided to retire the current coach of the Catalans, Luis Enrique, giving the club an ultimatum: either he or Enrique.

    According to the already mentioned English journalist Pete Jenson, it can hardly be said that Ronaldo and Messi exchanged characters. But they are no longer “as far apart at different ends of the personality spectrum as they were before.” If we “translate” from politically correct to understandable, it turns out: between the current Ronaldo and the current Messi from the point of view of ethics, the difference has been reduced to a minimum.

    “And what does morality have to do with it? – the reader will ask. – A football player should be judged by the game!”

    This is what the Spanish journalist Jorge Martinez told me about this.

    – When for the seventh year in a row the same two nominees reach the final of the fight for the Ballon d’Or, it is no secret to anyone what they can show on the field. Their capabilities, strikes and feints are thoroughly studied. If we take into account their approximately equal indicators in the game, then when voting, the decisive straw in the balance may be the moral qualities of Ronaldo and Messi.

    P.S. After Ronaldo was presented with the third Ballon d’Or, one of the FIFA functionaries complained on the sidelines: they say, over the past 7 years, the awards ceremony has become too predictable. If this worries even sports officials, then, apparently, they will soon start looking for a way out. The most original was offered by the famous Manchester United player Angel Di Maria. According to him, there is no doubt that Messi and Ronaldo are the best footballers in the world. Therefore, FIFA must present two Golden Ball awards.One will be challenged by Ronaldo and Messi, and the other by all the other players.

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    Elena Sushchinskaya – Lilith reveals her secrets: the return of the Black Moon.read online for free

    Elena Sushchinskaya

    LILITH REVEALS ITS MYSTERIES: THE RETURN OF THE BLACK MOON. INDEPENDENT INVESTIGATION

    Thanks in advance to the Black Moon for opening the veil of her secrets.

    This material was written on the basis of reports read by the author at the Fifth and Seventh International Astrological Conferences “Uranus in Aquarius” (Moscow, 2000 and 2002), and at the Ninth International Congress “Urania” “Myth and Symbol” (m / v ” Vladimir Mayakovsky “, Moscow – Perm, 2001), as well as on the basis of lectures given at the State Museum of the East in 2002

    A TALE ABOUT LOST TIME, or

    about the ordeals and exploits of the incarnate Soul

    Author’s Foreword

    This book is an attempt to rehabilitate the Black Moon, worthy of all kinds of honors, for it makes us all really work and, by and large, offers us a high level of creativity. Another thing is that such joint creativity with the Black Moon may not turn out to be to our liking due to our laziness, moral ill-being, disrespect for ethical laws.Nevertheless, it is the Black Moon that reveals the deepest and most difficult programs in us and makes us work, overcoming the inertia of our Ego. It shows us the most unsightly qualities, “pulls out” from us low-frequency states, all kinds of complexes, especially pride, selfhood. Our usual egoism, which has been “processed” by this fictitious point, ceases to torment others, and we become more tolerant, attentive, sensitive. The Black Moon makes us turn to face the world around us, and when we are too stubborn in our self, she, with the help of feedbacks, forces us to abandon the usual way of realizing this self.

    Preparing the material about the Black Moon, the author used exclusively the experience of practical work with this point, i.e. studying the fate of people and their relationship with the Black Moon through their horoscopes. At the same time, not a single source was specifically used where the Black Moon was mentioned. The reason for such a harsh condition is that in connection with the study of the influences on us of a fictitious point, a sufficient number of distortions have already been created, both in the interpretation of the Black Moon in horoscopes, and in the theoretical substantiation of the principles of its manifestation.In addition, the attempt of such an “independent investigation” is also due to the fact that, as a rule, when trying to make a generalized study of subtle substances and referring to a large amount of different information, we usually get significant distortions. Therefore, the author, taking responsibility, considered it possible to use the material obtained only through practical work with maps, without involving any additional information in connection with the indicated topic.

    This book is the result of ten years of practical work with the Black Moon.But, having the Black Moon in his natal chart (just like all earthlings), and having exhausted himself pretty much when solving her puzzles, the author, nevertheless, is not inclined to talk about his personal experience of meeting the Black Moon. Such experience was sufficiently shared with him by “eyewitnesses” – relatives, acquaintances, students and everyone who had the honor to come into close contact with the Black Moon in their lives.

    It is very difficult to write about the Black Moon or Lilith (hereinafter we will often call her that way), because it is always difficult to describe the “life” of subtle objects that have no confirmation in the world of dense forms.In this case, one has to use the data obtained through observing the course of a person’s individual karma, through comparing his efforts with the results he has obtained.

    I must say, Lilith does not accept fuss in the presentation of information about the implementation of her tasks. It requires a leisurely narration, thoroughness, many details, therefore, the text may contain repetitions of the same idea in different contexts. When it comes to Lilith, we cannot describe her simply, hastily.A simple presentation usually gives a shallow insight into the essence of any issue related to it. Therefore, in the book there will be repetitions, clarifications, which will make the material in some cases quite difficult, but the need to fully disclose the topic of Lilith makes the author take responsibility for the weight and some cumbersomeness in the presentation of the secrets of Lilith.

    Chapter 1. TALE ABOUT LOST TIME

    Reflections on the Black Moon

    Studying the Black Moon, you always want to shout: “No, it does not work, because it is not manifested, which means that there are no problems indicated by this point.There is no representative of the Black Moon in the material world. All this was thought up by careless astrologers! ” Nevertheless, Lilith “works”. In addition, the problems proposed by her are very serious and sometimes not solvable at all, although in the Solar System there really is no representative of the Black Moon in dense matter, which would confirm its existence.

    I must say that the tasks designated by Lilith often turn out to be too much for us, and we begin to feel fear of them, recognizing their fatality.Although many in our century already understand that the concept of fatality exists mainly only for idlers who do not want to be held responsible for their actions.

    After such an introduction, there is a natural need to learn how to work with Lilith and how to achieve positive results when interacting with her? Moreover, questions arise: is it possible to find a positive aspect of the work of the Black Moon at all, and how can we “agree” with this fictitious “object” of our reality without too distorting the principles of its manifestation?

    To answer all these questions it is necessary, first of all, to make a journey into the “past of our Past” and understand how this point was formed, what subtle substance was involved in its creation, and then try to trace the mechanism of its work.It must be said that to resolve the issues identified by Lilith, taking into account only the aspects of the present day, i.e. taking into account the indicated cause-and-effect relationships of the current incarnation, it is impossible. This point does not show our “today”, but always shows only past mistakes, albeit through “current” problems. This is the whole difficulty of understanding and working with Lilith, because the past means the present Past, i.e. past incarnations, about which we know little, and it looks like this.

    For example: Black Moon in the 10th house. In the current incarnation, this position may not bother a person with a pronounced need to organize and manage any structures, or the need to acquire a socially significant status. But it will certainly show that in the past it was this aspect that created ethical violations and, in connection with them, strong distortions in the spheres ruled by the 10th house. It is quite possible that now a person will be content with the so-called average social position and will not strive to take a leadership position anywhere, but he will almost always find himself next to such positions and there may be a lot of temptations in connection with them.His friends can occupy high positions, and at some time he himself will very much want to achieve a high position in society as well. Perhaps his loved ones will begin to very actively develop the topic of promotion, and the owner of Lilith in the 10th house will also want to do everything possible to move up the career ladder. But, as a rule, having sometimes reached a sufficiently high level, a person is forced to leave his position either of his own free will, or under the pressure of circumstances that have arisen in a completely incomprehensible way out of place and out of time.Although, perhaps, he will take the chair of the president of some company, if his life is conscious enough.

    Read more

    what kind of animal and how do they prepare it / Habr

    Link to the source – there is more order with the design, especially for videos.

    Contents

    Es ist noch kein Meister vom Himmel gefallen,
    or
    Not gods burn pots

    Russian-German proverb

    Introduction

    Here we tell about the Robotics and Mechatronics Center (RMC) of the National Center for Aviation and Astronautics of Germany.In the original language, it all sounds like this: Robotik und Mechatronik Zentrum (the abbreviation is used in English, RMC) and Deutsches Zentrum für Luft- und Raumfahrt (the abbreviation is used in German, DLR).

    DLR RMC is not as well known to the general public as, for example, Boston Dynamics, which we talked about earlier. Nevertheless, I am sure that you probably know the developments of the Center if you have any interest in robotics. In the first part, we talked about how these developments are related to space and about what RMC has become famous in the field of robotics in general.Here, let’s just pull back the veil from an interesting approach to building control systems for robots, which allowed RMC scientists and engineers to achieve the results that we can observe today. It has found application in many projects of the Center, which have become widely known not only in robotic circles.

    This is impedance control .

    This material was born because the idea arose to share what I saw and heard personally.Just like that, without having my own face-to-face experience, it would be more difficult to collect all this information in a heap. So, I think the material should be interesting not only to me. And if he also helps someone to take the first, most difficult step to robotic heights in this direction, then I will consider this my achievement too.

    About concepts

    The problem of control in engineering is the construction of a regulator that meets the given criteria of control quality. In this article, using the available publications [1], we will just describe how regulators are built that provide RMC robots with their remarkable qualities.

    Let’s first clarify what kind of animal this is – impedance control . Here it is important for us to understand the principle. We will not write program code, because a specific implementation is a personal, intimate matter for each developer. Well, and you – go for it!

    Mechanical impedance control [2], in simple terms, endows the manipulator with the properties of a spring-damper system with rigidity and damping coefficient adjustable according to an arbitrary law and in arbitrary coordinates.And when we talk about stiffness and damping with mechanical impedance control , we mean active stiffness and damping . Those. these virtual “spring” and “damper” do not actually exist physically, but are implemented by actuators, which distinguishes them from real links and joints with (passive) compliance.

    LBR iiwa. The term compliance is used here, not impedance. Well, marketers know better what is closer to users

    It seems that all work on mechanical impedance control refers to MIT professor Neville Hogan [3].Considering the traditional methods of controlling industrial manipulators, he distinguishes among them two well-known approaches that combine the ability to neglect the dynamic interaction between the manipulator and the external environment. In the first case, when there is no contact with external objects, the interaction forces are equal to zero, and control along the coordinate (position or speed) can be realized. In essence, the manipulator is considered here as an isolated system. In the second case, when there is no movement on contact with a solid object, algorithms of force control can be used.In both cases, the mechanical work performed by the manipulator is zero: dW = F × dX = 0 .

    In the general case, the mutual influence of the manipulator and the environment cannot be neglected, because they interact with each other, exchanging mechanical energy ( dW ≠ 0 ), which means that the manipulator can no longer be considered as an isolated system. In each degrees of freedom , the instantaneous power of this interaction is defined as the product of two conjugate variables: forces (for example, force or torque; electric voltage; etc.). and displacements (for example, movement speed; current strength; etc.). As a result, it becomes insufficient to manage any one variable.

    Hogan proposes a unified approach that includes the above as particular solutions. Continuing the analogy with electricity, he considers two kinds of properties that physical systems have: impedance and admittance . These concepts are familiar to electrical engineers as mutually inverse parameters of electrical circuits: complex resistance and complex conductivity. For systems described in terms of admittance , the input is force and the output is displacement . Conversely, for systems described in terms of impedance , the input is displacement and the output is force . In the case of linear systems , the systems of equations describing them can be expressed both in terms of impedance and in terms of admittance . Non-linear systems can be described either through impedance , or through admittance , i.e.That is, these parameters are not interchangeable for them.

    Note that the control of industrial manipulators (their mechanical part) is traditionally considered in terms of admittance , since it is intended to implement the given law of displacement of manipulator links (at the output) by regulating, ultimately, efforts of drives (at the input of the mechanical parts).

    It is important that in the case of dynamic interaction of physical systems, they must complement each other: if one of them is impedance , the second must be admittance .For example, if the manipulator interacts with external objects that have inertia, which is linear expression of the relationship between the acting force and the change in the measure of displacement, then physically this manifests itself in the form of applying forces to the objects , forcing them to move (external environment – admittance ). However, if a manipulator is described in the form admittance , then the external environment may well be represented as impedance , i.e.Because, knowing displacement , you can calculate force . If the object has kinematic restrictions, then you can still apply force to it, but it will not necessarily lead to displacement, i.e. the description of its movement becomes non-linear . This means that it becomes impossible to unambiguously calculate the displacement effort.

    Thus, in the general case, the behavior of an external object can only be correctly described in terms of admittance .And to be impedance remains the manipulator. Because of the two of them, , someone has to yield to , and this is not an external object.

    And here you can!

    Now, armed with the knowledge that in general the impedance of should be a manipulator, let’s see how this approach is implemented in the DLR RMC.

    Model of dynamics

    The following equation is known in robotics [4], which describes in matrix form the dynamics of the mechanical part of the manipulator in space generalized coordinates q :

    (1)

    So that it does not seem scary, but in order not to get into the literature, which will make it even worse because of multi-storey matrix calculations, we will explain how you can quickly understand such equations.

    The right side is the sum of the forces acting on the links of the manipulator, specified by the column vector τ forces / torques from the side of the drives and the column vector τ ext forces / moments from the external environment. All components of these generalized forces (i.e. elements of the column vectors) are specified in the coordinate systems of the corresponding joints of the manipulator, i.e. in the space generalized coordinates .

    The left side of the equation is where this effort is “spent”.The first term is the product of the matrix M (q) masses and moments of inertia of the manipulator links by the column vector of accelerations in its joints (recall Newton’s second law). The second term takes into account centrifugal and Coriolis forces proportional to the velocities, i.e. fictitious forces, which, as it were, do not exist in nature, appearing in the equation only because it is more convenient for us to carry out calculations in systems of generalized coordinates, which for rotational joints are rotating (i.e., non-inertial).Well, the third term is the column vector g (q) of the gravitational forces acting on the joints for the current configuration (position) of the manipulator q .

    So, the sum of all the forces acting in the joints of the manipulator is spent on overcoming the force of gravity and on imparting acceleration to its links . As you can see, everything is very clear.

    LWR III manipulator and its hinge model

    Now let’s see what the manipulator hinge is.As we discussed above, the RMC arms have significant flexibility, which is reflected in the hinge model. In the above diagram, B denotes the moment of inertia of the motor rotor, M is the link mass, and K is the stiffness of the elastic element in the hinge. The rotor is driven into rotation by a torque of τ m , and a force F ext (in some base coordinate system) acts on the link from the external environment. The rotor motion equation is as follows:

    , (2)

    where θ is the angular position from the motor side.

    Again we read the equation: the electromagnetic moment of the motor τ m drives the rotor into rotation (the first term is the equivalent of the same second Newton’s law for rotational motion), and also creates a moment τ on the manipulator link. This moment is transmitted to the link through the “spring” of the hinge, therefore it is proportional to the angle of twisting of the “spring” (Hooke’s law), i.e. difference of angles from the motor side θ and from the link side q :

    (3)

    Expressions (2) and (3) , as well as expression (1) , are written in matrix form.Let us also make a reservation that, although the arguments here and below are given by the example of rotational motions, they are also valid for the general case, i.e. for any type of joints (translational, rotational and any combination of them).

    Generalized impedance control

    we agreed to build a regulator with controlled stiffness and damping, consider its scheme. As can be seen in the figure, elements corresponding to the stiffness coefficients K θ and damping D θ of the regulator have been added to the above hinge model.Also added was the image of the feedback at the moment τ (shown by the dotted line), which will be discussed below.

    Hinge model with a mass-spring-damper regulator

    Since we are talking about a software regulator, we can implement any desired control law. Based on the given scheme of the regulator of the “mass – spring – damper” type, the control law should be as follows:

    ) corresponds to the twist angle of the virtual regulator spring.The second term in the equation responsible for damping, in accordance with the well-known model of viscous friction, is proportional to the twisting speed. A minus sign in front of it means the desire to reduce (damp) the engine speed.

    Looking at the equation, we can see that we have, in fact, a PD controller for the angle of rotation of the engine. Having accepted

    , we write the equation in the following form:

    (4)

    To ensure high-quality control of the flexible joint with the help of a “flexible” regulator, it is important to reduce the inertia of the intermediate mass element (in this case, the motor rotor).Otherwise, the resulting movement may differ significantly from the desired one. Not being able to reduce the real moment of inertia of the rotor, we, nevertheless, can “reduce” it artificially by introducing torque feedback. Since, we repeat, all control laws are implemented in software, we can implement the following feedback by adjusting the motor torque τ m using the internal current loop:

    , (5)

    where B θ – the desired moment of inertia of the rotor, and I is the identity matrix (we are still recording in matrix form).If we now substitute the equation (5) into (2) , then we can get:

    (6)

    We see that, from the point of view of the upper level, the system (6) with feedback ( 5) is similar to the system (2) without feedback, for which we would independently choose an arbitrary moment of inertia of the rotor B θ and the desired law of variation of the motor torque u .

    Generalized impedance control

    Summarize. Equation (4) defines the required controller with arbitrary matrices of stiffness and damping coefficients, which implements in generalized coordinates the control of mechanical impedance for a given desired law of motion of the system described by equations (1) , (6) , (3) , subject to the implementation of internal feedback (5) at the moment . Let us write out the resulting system of equations.

    System dynamics equations:

    (I)

    Internal loop controller equation:

    (II)

    Controller equation for impedance control in generalized coordinates (

    73) III

    Note also that at this stage the knowledge of the manipulator dynamics model is not necessary.It would seem that we implement the feedback of the inner loop (II) , build the regulator (III) , choosing its coefficients K θ and D θ , and then control it by setting the desired law of variation of the coordinate θ d . The dynamics model will be needed below, and here its equations are given to understand the process.

    Impedance control in Cartesian coordinates

    In practice, it is often more convenient to set the desired control law not in generalized, but in basic (for example, Cartesian) coordinates.Knowing the solution of the direct problem of kinematics, it is possible to find the column vector of the Cartesian coordinates of the output link of the manipulator and the corresponding Jacobi matrix as a function of the coordinates of the links – x (q), J (q) – and the coordinates of the motors – x (θ), J (θ ) :

    ,

    ,

    Impedance control in Cartesian coordinates

    As we remember from the discussion of expression (6) , the control signal u in equation (4) has the physical meaning of the desired torque motor, and its terms are responsible, respectively, for the components of the virtual spring ( τ K ) and the virtual damper ( τ D ).Taking into account [5] that

    ,

    , you can write the equation of the controller (4) in Cartesian coordinates, converting the moments in the joints into forces on the output link:

    ,

    or:

    , (7)

    where K x and D x are the matrices of the stiffness and damping coefficients of the manipulator in Cartesian coordinates, and

    is the column vector taken with the opposite sign of the deviations of the current coordinates of the output link from the desired d .Finally, differentiating the expression for x (θ) in time, we get:

    Thus, to control the mechanical impedance in Cartesian coordinates in the system of equations (I), (II), (III) needs only to be replaced regulator equations (III) in generalized coordinates to equations (IV) written in the form (7) :

    (IV)

    Now the matrix of stiffness coefficients K x and damping D x as well as the column vector x d of the desired manipulator movement can be specified in Cartesian coordinates.

    Gravity Compensation

    So far, gravity has not been taken into account in the equations for the controller. Nevertheless, in the case of an elastic drive, it must be taken into account. This is done by dividing the reference signal into components, one of which actually controls the movement (as described above), and the other only compensates for the effect of gravity. The RMC articles indicate that a good result can be achieved in the case of calculating the compensating component in coordinates from the engine side based on the condition of the steady state of equilibrium .

    Aline Albu-Schaeffer separately demonstrates the gravity compensation mode: the Justin robot moves freely under the influence of external forces

    Equilibrium condition in which the elastic force arising from the twisting of the “spring” of the hinge balances the gravity force from the link, for some equilibrium coordinates θ 0 , q 0 (respectively, from the engine side and from the link side) can be written as follows:

    where g (q 0 ) is a column vector of forces caused by gravity and acting on the joints, calculated for the manipulator configuration q 0 – see.equation (1) . We know the expression for g (q) from the manipulator dynamics model. Actually, here for the first time we needed knowledge of the dynamics model to take it directly into account in the controller equations.

    Based on this equilibrium condition, we find a compensating addition u g the dimensions of the motor torque for the equations (4), (7) of the control signal u :

    ,

    ,

    New designations introduced here are used for ease of notation to show that the compensating addition u g can be expressed as a function of the angle θ .

    Gravity compensation mode for LBR iiwa

    Let us now write a system of equations describing the dynamics of the manipulator and the regulator for impedance control, taking into account the component for gravity compensation :

    System dynamics equations:

    (I)

    Internal loop controller equation:

    (II)

    Controller equation to control the impedance in generalized coordinates :

    (V)

    Equation to control the impedance of the controller :

    (VI)

    And also the dynamics model allows you to select external forces on the links of the robot (for example, in order to implement the control mode of external forces for safe joint work with a person)

    Visco- elastic hinges 903 30

    Now, finally, we can give a general block diagram of a regulator for controlling mechanical impedance, the equations of which we have been deriving all this time:

    A regulator for controlling mechanical impedance in Cartesian coordinates

    It would seem that this is all? Not really.It seems that all the variables on the diagram are already known to us and correspond to the above equations. In addition to the output torque τ a . But our equations contain τ . What is the difference? Take a look at the hinge model shown at the beginning of the article. Do you see the stiffener K in it between the rotor B and the link M ? And on the regulator circuit, a damper D was added to it. Because the model of the hinge can take into account not only its elastic, but also its damping properties:

    Here the component τ K , in accordance with (3) , is proportional to the torsion angle of the “spring” of the hinge,

    ,

    a τ D (viscous friction) – twisting speeds,

    Denoting the usual τ = τ K , it is easy to show that:

    ,

    ,

    and then

    the model of the dynamics of the system (I) will be written in the form [6]:

    (VII)

    Well, now, it seems, everything.

    Complex Impedance Control Modes for Justin Robot. “Coupled spatial impedance” – virtual spatial spring: between the grips of the “hands”; “Attached” to the manipulation object

    Conclusion

    Recalling the division of methods for constructing control systems for robots into two conditional groups, “classical” and “practical”, discussed in the article about Boston Dynamics, we can confidently classify the approach considered here as “.It does not contradict the theoretically developed coordinate control methods traditionally used for industrial manipulators, but complements them. Meticulous Germans have developed algorithms in an analytical form, conducted their detailed analysis, and proved their stability.

    Not everything is included in this article. Here we only considered the idea itself, which has proven its efficiency. So our guys at the Central Research Institute of RTK in 2016 managed to build the first working version of the manipulator with impedance control [7].It seems that the first turned out to be the last, but that’s another story. The main thing is what happened!

    Maintaining a given vertical force

    “Flow” around an obstacle

    Manipulator-spring

    And even with flaws, but the pin crawls into the hole!

    Well, RMC did not stop there and continued to develop impedance control algorithms [8]. The proof of this is the robot David, which studies impedance control now for flexible actuators that are specially designed flex.In contrast to traditional flexible arms, in which compliance is a forced result of weight loss activities.

    Robot David: ESπ- (ESP-) control – the next step in the development of mechanical impedance control algorithms

    If we talk about the development of domestic robotics, then it is worth learning from the best world examples, such as the example of RMC. An attempt was made here not to write formulas boringly, but to make them understandable. When a person understands the idea, becomes interested, then further he will figure out the details himself (and then he will complicate everything back to any degree of boringness).So let the serious uncles of mathematics and physics forgive me for the liberties allowed in the reasoning, if this text can inspire some of the novice (or not very beginner) robotics who are making their way to a great future!


    1. ↑ See, for example: A Passivity Based Cartesian Impedance Controller for Flexible Joint Robots – Part I: Torque Feedback and Gravity Compensation,
      On the Passivity-Based Impedance Control of Flexible Joint Robots,
      A Unified Passivity-based Control Framework for Position, Torque and Impedance Control of Flexible Joint Robots
      and etc.
    2. ↑ Impedance control – Wikipedia
    3. ↑ N. Hogan. Impedance Control: An Approach to Manipulation: Part 1 – Theory, Part II – Implementation, Part III – Applications
    4. ↑ See, for example: Shahinpur, M.

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