Display with robotic pixels

• US 8,723,872 B2
• Filed: 06/08/2011
• Issued: 05/13/2014
• Est. Priority Date: 06/09/2010
• Status: Active Grant

• Current Assignee: ETH Zurich, Disney Enterprises Incorporated (The Walt Disney Company)
• Original Assignee: Disney Enterprises Incorporated (The Walt Disney Company)
• Inventors: Beardsley, Paul, Mora, Javier Alonso, Breitenmoser, Andreas, Rufli, Martin, Siegwart, Roland, Matthews, Iain, Yamane, Katsu
• Primary Examiner(s): Tung, Kee M
• Assistant Examiner(s): CHEN, FRANK S
• Application Number:
  US13/156,212
• Publication Number:
  US 20110304633A1
• Time in Patent Office: 1,070 Days
• Field of Search: None
• US Class Current: 345/474
• CPC Class Codes: B25J 9/1666 Avoiding collision or forbidden zones
• CPC Class Codes: G06T 13/80 2D [Two Dimensional] animation, e.g. using sprites
• CPC Class Codes: Y10S 901/01 Mobile robot
• CPC Class Codes: Y10S 901/46 Sensing device

Abstract

Techniques are disclosed for controlling robot pixels to display a visual representation of an input. The input to the system could be an image of a face, and the robot pixels deploy in a physical arrangement to display a visual representation of the face, and would change their physical arrangement over time to represent changing facial expressions. The robot pixels function as a display device for a given allocation of robot pixels. Techniques are also disclosed for distributed collision avoidance among multiple non-holonomic robots to guarantee smooth and collision-free motions. The collision avoidance technique works for multiple robots by decoupling path planning and coordination.

Claims

1. A method for controlling multiple non-holonomic robotic elements, comprising:

increasing a radius associated with each non-holonomic robotic element by a respective maximum tracking error value with respect to a trajectory of a holonomic robotic element to generate a set of modified radii;

generating a set of collision-free velocities based on (i) the set of modified radii, a (ii) first set of allowed holonomic velocities for each robotic element of multiple holonomic robotic elements, and (iii) a second set of collision-free velocities for each robotic element of the multiple holonomic robotic elements relative to neighboring robotic elements of the multiple holonomic robotic elements, wherein each robotic element of the multiple holonomic robotic elements is associated with a respective robotic element of the multiple non-holonomic robotic elements;

selecting an optimal holonomic velocity for each robotic element of the multiple holonomic robotic elements from the set of collision-free velocities; and

mapping the optimal holonomic velocity for each robotic element of the multiple holonomic robotic elements to each respective robotic element of the multiple non-holonomic robotic elements to generate inputs for controlling collision-free movement of the multiple non-holonomic robotic elements.

2. The method of claim 1, wherein the inputs are selected to minimize a respective tracking error that is computed based on a trajectory of each non-holonomic robot element of the multiple non-holonomic robotic elements.

3. The method of claim 2, wherein the tracking error of each non-holonomic robot element of the multiple non-holonomic robotic elements is less than or equal to the maximum tracking error value for the respective non-holonomic robot element of the multiple non-holonomic robotic elements.

4. The method of claim 2, wherein the trajectory of each non-holonomic robotic element is modified by an external input device.

5. The method of claim 1, further comprising approximating the first set of allowed holonomic velocities for each robotic element of multiple holonomic robotic elements by a convex polygon that lies within the first set of allowed holonomic velocities for each robotic element of multiple holonomic robotic elements and is aligned with a current orientation of the respective robotic element of multiple holonomic robotic elements.

6. A non-transitory computer-readable storage medium including instructions that, when executed by a processor, cause the processor to control multiple non-holonomic robotic elements, by performing the steps of:

increasing a radius associated with each non-holonomic robotic element by a respective maximum tracking error value with respect to a trajectory of a holonomic robotic element to generate a set of modified radii;

generating a set of collision-free velocities based on (i) the set of modified radii, (ii) a first set of allowed holonomic velocities for each robotic element of multiple holonomic robotic elements, and (iii) a second set of collision-free velocities for each robotic element of the multiple holonomic robotic elements relative to neighboring robotic elements of the multiple holonomic robotic elements, wherein each robotic element of the multiple holonomic robotic elements is associated with a respective robotic element of the multiple non-holonomic robotic elements;

selecting an optimal holonomic velocity for each robotic element of the multiple holonomic robotic elements from the set of collision-free velocities; and

mapping the optimal holonomic velocity for each robotic element of the multiple holonomic robotic elements to each respective robotic element of the multiple non-holonomic robotic elements to generate inputs for controlling collision-free movement of the multiple non-holonomic robotic elements.

7. The non-transitory computer-readable storage medium of claim 6, wherein the inputs are selected to minimize a respective tracking error that is computed based on a trajectory of each non-holonomic robot element of the multiple non-holonomic robotic elements.

8. The non-transitory computer-readable storage medium of claim 7, wherein the tracking error of each non-holonomic robot element of the multiple non-holonomic robotic elements is less than or equal to the maximum tracking error value for the respective non-holonomic robot element of the multiple non-holonomic robotic elements.

9. The non-transitory computer-readable storage medium of claim 8, wherein the trajectory of each non-holonomic robotic element is modified by an external input device.

10. The non-transitory computer-readable storage medium of claim 6, further comprising approximating the first set of allowed holonomic velocities for each robotic element of multiple holonomic robotic elements by a convex polygon that lies within the first set of allowed holonomic velocities for each robotic element of multiple holonomic robotic elements and is aligned with a current orientation of the respective robotic element of multiple holonomic robotic elements.

11. A system for controlling multiple non-holonomic robotic elements, comprising:

a memory that is configured to store instructions for a program; and

a processor that is configured to execute the instructions for the program to control the multiple non-holonomic robotic elements by performing an operation, the operation comprising;

increasing a radius associated with each non-holonomic robotic element by a respective maximum tracking error value with respect to a trajectory of a holonomic robotic element to generate a set of modified radii;

generating a set of collision-free velocities based on (i) the set of modified radii, (ii) a first set of allowed holonomic velocities for each robotic element of multiple holonomic robotic elements, and (iii) a second set of collision-free velocities for each robotic element of the multiple holonomic robotic elements relative to neighboring robotic elements of the multiple holonomic robotic elements, wherein each robotic element of the multiple holonomic robotic elements is associated with a respective robotic element of the multiple non-holonomic robotic elements;

selecting an optimal holonomic velocity for each robotic element of the multiple holonomic robotic elements from the set of collision-free velocities; and

mapping the optimal holonomic velocity for each robotic element of the multiple holonomic robotic elements to each respective robotic element of the multiple non-holonomic robotic elements to generate inputs for controlling collision-free movement of the multiple non-holonomic robotic elements.

12. The system of claim 11, wherein the inputs are selected to minimize a respective tracking error that is computed based on a trajectory of each non-holonomic robot element of the multiple non-holonomic robotic elements.

13. The system of claim 12, wherein the tracking error of each non-holonomic robot element of the multiple non-holonomic robotic elements is less than or equal to the maximum tracking error value for the respective non-holonomic robot element of the multiple non-holonomic robotic elements.

14. The system of claim 12, wherein the trajectory of each non-holonomic robotic element is modified by an external input device.

15. The system of claim 11, further comprising approximating the first set of allowed holonomic velocities for each robotic element of multiple holonomic robotic elements by a convex polygon that lies within the first set of allowed holonomic velocities for each robotic element of multiple holonomic robotic elements and is aligned with a current orientation of the respective robotic element of multiple holonomic robotic elements.