Evaluating Form Closure Project - Revision history

Lynch: /* Program Specification */

2018-07-20T11:03:46Z

Program Specification

← Older revision		Revision as of 06:03, 20 July 2018
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	You will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure. Your program will likely use linear programming, as described in Chapter 12.1.7 in '''[http://modernrobotics.org the book]'''. In MATLAB, the function is called linprog. In Mathematica, it is LinearProgramming. In Python, it is scipy.optimize.linprog.		You will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure. Your program will likely use linear programming, as described in Chapter 12.1.7 in '''[http://modernrobotics.org the book]'''. In MATLAB, the function is called linprog. In Mathematica, it is LinearProgramming. In Python, it is scipy.optimize.linprog.

	: '''Important note for Python users:''' A Coursera student mentioned a bug in linprog, apparently occurring when using the 'simplex' method for solving linear programs where the equality constraints are specified by a matrix that is not full rank. One solution is to use the interior point method by adding the option "method='interior-point'". See the discussion at [https://github.com/scipy/scipy/issues/6690 https://github.com/scipy/scipy/issues/6690].		: '''Important note for Python users:''' A Coursera student mentioned a bug in an earlier version of linprog, apparently occurring when using the 'simplex' method for solving linear programs where the equality constraints are specified by a matrix that is not full rank. One solution is to use the interior point method by adding the option "method='interior-point'". See the discussion at [https://github.com/scipy/scipy/issues/6690 https://github.com/scipy/scipy/issues/6690].

	(Although your program will be written for planar form closure [to allow you to intuitively compare your results to those achieved using graphical methods], it is trivial to extend your program to spatial form closure.)		(Although your program will be written for planar form closure [to allow you to intuitively compare your results to those achieved using graphical methods], it is trivial to extend your program to spatial form closure.)

Lynch: /* Program Specification */

2018-07-20T10:58:44Z

Program Specification

← Older revision		Revision as of 05:58, 20 July 2018
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	You will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure. Your program will likely use linear programming, as described in Chapter 12.1.7 in '''[http://modernrobotics.org the book]'''. In MATLAB, the function is called linprog. In Mathematica, it is LinearProgramming. In Python, it is scipy.optimize.linprog.		You will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure. Your program will likely use linear programming, as described in Chapter 12.1.7 in '''[http://modernrobotics.org the book]'''. In MATLAB, the function is called linprog. In Mathematica, it is LinearProgramming. In Python, it is scipy.optimize.linprog.

			: '''Important note for Python users:''' A Coursera student mentioned a bug in linprog, apparently occurring when using the 'simplex' method for solving linear programs where the equality constraints are specified by a matrix that is not full rank. One solution is to use the interior point method by adding the option "method='interior-point'". See the discussion at [https://github.com/scipy/scipy/issues/6690 https://github.com/scipy/scipy/issues/6690].

	(Although your program will be written for planar form closure [to allow you to intuitively compare your results to those achieved using graphical methods], it is trivial to extend your program to spatial form closure.)		(Although your program will be written for planar form closure [to allow you to intuitively compare your results to those achieved using graphical methods], it is trivial to extend your program to spatial form closure.)

Lynch: /* Program Specification */

2018-07-04T04:54:37Z

Program Specification

← Older revision		Revision as of 23:54, 3 July 2018
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	You will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure. Your program will likely use linear programming, as described in Chapter 12.1.7 in '''[http://modernrobotics.org the book]'''. In MATLAB, the function is called linprog. In Mathematica, it is LinearProgramming. In Python, it is scipy.optimize.linprog.		You will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure. Your program will likely use linear programming, as described in Chapter 12.1.7 in '''[http://modernrobotics.org the book]'''. In MATLAB, the function is called linprog. In Mathematica, it is LinearProgramming. In Python, it is scipy.optimize.linprog.

	(Although your program will be written for planar form closure (to allow you to intuitively compare your results to those achieved using graphical methods), it is trivial to extend your program to spatial form closure.)		(Although your program will be written for planar form closure [to allow you to intuitively compare your results to those achieved using graphical methods], it is trivial to extend your program to spatial form closure.)

	Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction should be specified by a single number (the angle of the inward-pointing normal, in degrees or radians, relative to the positive <math>x</math>-axis). Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.		Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction should be specified by a single number (the angle of the inward-pointing normal, in degrees or radians, relative to the positive <math>x</math>-axis). Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.

Lynch at 22:40, 27 May 2018

2018-05-27T22:40:10Z

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	This page describes the "Evaluating Form Closure" Project from the Coursera course "Modern Robotics, Course 5: Robot Manipulation and Wheeled Mobile Robots."		This page describes the "Evaluating Form Closure" Project from the Coursera course "Modern Robotics, Course 5: Robot Manipulation and Wheeled Mobile Robots."

	=== Introduction ====		=== Introduction ===

	In this programming assignment, you will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure.		In this programming assignment, you will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure.

Lynch at 22:40, 27 May 2018

2018-05-27T22:40:01Z

← Older revision		Revision as of 17:40, 27 May 2018
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	This page describes the "Evaluating Form Closure" Project from the Coursera course "Modern Robotics, Course 5: Robot Manipulation and Wheeled Mobile Robots."		This page describes the "Evaluating Form Closure" Project from the Coursera course "Modern Robotics, Course 5: Robot Manipulation and Wheeled Mobile Robots."

			=== Introduction ====

			In this programming assignment, you will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure.

			Your assignment will be graded based on:
			* An evaluation of your source code, including its clarity for the reader.
			* The correctness of your code's output on two sets of example contacts that you create. You will also provide drawings corresponding to the two cases, showing the feasible twist cone (drawn as centers of rotation) corresponding to the contacts in each case, confirming your code's output.

	=== Program Specification ===		=== Program Specification ===

Lynch: /* Program Specification */

2018-05-05T16:00:06Z

Program Specification

← Older revision		Revision as of 11:00, 5 May 2018
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	(Although your program will be written for planar form closure (to allow you to intuitively compare your results to those achieved using graphical methods), it is trivial to extend your program to spatial form closure.)		(Although your program will be written for planar form closure (to allow you to intuitively compare your results to those achieved using graphical methods), it is trivial to extend your program to spatial form closure.)

	Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction should be specified by a single number (the angle of the inward-pointing normal, in degrees or radians, relative to the <math>+x</math>-axis). Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.		Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction should be specified by a single number (the angle of the inward-pointing normal, in degrees or radians, relative to the positive <math>x</math>-axis). Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.

	The output of your program will be binary: the body is either in form closure or not in form closure. If the body is in form closure, it is also recommended that you output the solution to the linear program. This will be a (nonunique) vector <math>k</math> of nonnegative wrench magnitudes at the contacts such that the sum of contact wrenches on the body is zero. (See Example 12.7 in the book.)		The output of your program will be binary: the body is either in form closure or not in form closure. If the body is in form closure, it is also recommended that you output the solution to the linear program. This will be a (nonunique) vector <math>k</math> of nonnegative wrench magnitudes at the contacts such that the sum of contact wrenches on the body is zero. (See Example 12.7 in the book.)

Lynch: /* Program Specification */

2018-05-05T15:59:42Z

Program Specification

← Older revision		Revision as of 10:59, 5 May 2018
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	(Although your program will be written for planar form closure (to allow you to intuitively compare your results to those achieved using graphical methods), it is trivial to extend your program to spatial form closure.)		(Although your program will be written for planar form closure (to allow you to intuitively compare your results to those achieved using graphical methods), it is trivial to extend your program to spatial form closure.)

	Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction should be specified by a single number (the angle of the inward-pointing normal, in degrees or radians). Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.		Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction should be specified by a single number (the angle of the inward-pointing normal, in degrees or radians, relative to the <math>+x</math>-axis). Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.

	The output of your program will be binary: the body is either in form closure or not in form closure. If the body is in form closure, it is also recommended that you output the solution to the linear program. This will be a (nonunique) vector <math>k</math> of nonnegative wrench magnitudes at the contacts such that the sum of contact wrenches on the body is zero. (See Example 12.7 in the book.)		The output of your program will be binary: the body is either in form closure or not in form closure. If the body is in form closure, it is also recommended that you output the solution to the linear program. This will be a (nonunique) vector <math>k</math> of nonnegative wrench magnitudes at the contacts such that the sum of contact wrenches on the body is zero. (See Example 12.7 in the book.)

Lynch: /* Program Specification */

2018-05-05T15:59:01Z

Program Specification

← Older revision		Revision as of 10:59, 5 May 2018
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	(Although your program will be written for planar form closure (to allow you to intuitively compare your results to those achieved using graphical methods), it is trivial to extend your program to spatial form closure.)		(Although your program will be written for planar form closure (to allow you to intuitively compare your results to those achieved using graphical methods), it is trivial to extend your program to spatial form closure.)

	Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction should be specified by a single number (~~e.g.,~~ the angle of the inward-pointing normal, in degrees or radians). Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.		Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction should be specified by a single number (the angle of the inward-pointing normal, in degrees or radians). Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.

	The output of your program will be binary: the body is either in form closure or not in form closure. If the body is in form closure, it is also recommended that you output the solution to the linear program. This will be a (nonunique) vector <math>k</math> of nonnegative wrench magnitudes at the contacts such that the sum of contact wrenches on the body is zero. (See Example 12.7 in the book.)		The output of your program will be binary: the body is either in form closure or not in form closure. If the body is in form closure, it is also recommended that you output the solution to the linear program. This will be a (nonunique) vector <math>k</math> of nonnegative wrench magnitudes at the contacts such that the sum of contact wrenches on the body is zero. (See Example 12.7 in the book.)

Lynch: /* Program Specification */

2018-05-05T15:57:51Z

Program Specification

← Older revision		Revision as of 10:57, 5 May 2018
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	You will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure. Your program will likely use linear programming, as described in Chapter 12.1.7 in '''[http://modernrobotics.org the book]'''. In MATLAB, the function is called linprog. In Mathematica, it is LinearProgramming. In Python, it is scipy.optimize.linprog.		You will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure. Your program will likely use linear programming, as described in Chapter 12.1.7 in '''[http://modernrobotics.org the book]'''. In MATLAB, the function is called linprog. In Mathematica, it is LinearProgramming. In Python, it is scipy.optimize.linprog.

			(Although your program will be written for planar form closure (to allow you to intuitively compare your results to those achieved using graphical methods), it is trivial to extend your program to spatial form closure.)

	Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction should be specified by a single number (e.g., the angle of the inward-pointing normal, in degrees or radians). Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.		Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction should be specified by a single number (e.g., the angle of the inward-pointing normal, in degrees or radians). Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.

Lynch at 21:46, 1 May 2018

2018-05-01T21:46:49Z

← Older revision		Revision as of 16:46, 1 May 2018
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	You will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure. Your program will likely use linear programming, as described in Chapter 12.1.7 in '''[http://modernrobotics.org the book]'''. In MATLAB, the function is called linprog. In Mathematica, it is LinearProgramming. In Python, it is scipy.optimize.linprog.		You will write a program to determine if a planar rigid body, subject to a specified set of stationary point contacts, is in form closure. Your program will likely use linear programming, as described in Chapter 12.1.7 in '''[http://modernrobotics.org the book]'''. In MATLAB, the function is called linprog. In Mathematica, it is LinearProgramming. In Python, it is scipy.optimize.linprog.

	Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction ~~can~~ be specified by a single number (e.g., the angle of the inward-pointing normal, in degrees or radians) ~~or by a 2-vector, as you prefer~~. Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.		Your program will take as input a list of stationary point contacts on the body, each specified by the <math>(x,y)</math> contact location and the direction of the contact normal. The contact normal direction should be specified by a single number (e.g., the angle of the inward-pointing normal, in degrees or radians). Ideally the input would be in the form of arguments to your function, or would be read from an external input file that is easily edited.

	The output of your program will be binary: the body is either in form closure or not in form closure. If the body is in form closure, it is also recommended that you output the solution to the linear program. This will be a (nonunique) vector <math>k</math> of nonnegative wrench magnitudes at the contacts such that the sum of contact wrenches on the body is zero. (See Example 12.7 in the book.)		The output of your program will be binary: the body is either in form closure or not in form closure. If the body is in form closure, it is also recommended that you output the solution to the linear program. This will be a (nonunique) vector <math>k</math> of nonnegative wrench magnitudes at the contacts such that the sum of contact wrenches on the body is zero. (See Example 12.7 in the book.)