US5294873A
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Kinematic functions for redundancy resolution using configuration control
Assignee: National Aeronautics and Space Administration
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Filing: 1992-10-27
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Granted: 1994-03-15
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Expires: 2012-10-27
Abstract
Abstract The invention fulfills new goals for redundancy resolution based on manipulator dynamics and end-effector characteristics. These goals are accomplished by employing the recently developed configuration control approach. Redundancy resolution is achieved by controlling the joint inertia matrix or the end-effector mass matrix that affect the inertial torques, or by reducing the joint torques due to gravity loading and payload. The manipulator mechanical-advantage and velocity-ratio are also used as performance measures to be improved by proper utilization of redundancy. Furthermore, end-effector compliance, sensitivity, and impulsive force at impact are introduced as redundancy resolution criteria. The new goals for redundancy resolution allow a more efficient utilization of the redundant joints based on the desired task requirements.
Inventors
- 👤 Homayoun Seraji
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-23 12:30
CPC Classifications
B; B25; B25J; B25J9/00; B25J9/16; B25J9/1628; B25J9/1638; B25J9/1643; G; G05; G05B; G05B2219/00; G05B2219/30; G05B2219/40; G05B2219/40342
Claims Analysis
Total Claims: 22
Claim 1
Independent Claim
162 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to a minimization of gravity loading on said joints, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of a gravity loading function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and, controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said minimization of gravity loading.
Claim 2
Independent Claim
162 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to a minimization of gravity loading on said joints, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of a gravity loading function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and, controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said minimization of gravity loading.
Claim 3
Dependent Claim
45 words
The method of claim 1 wherein said gravity loading function is a function of the angles of all of said n joints and comprises a sum over all of said n joints of squares of elements of a vector of gravity loading on respective joints.
Claim 4
Dependent Claim
39 words
The method of claim 2 wherein said gravity loading function is defined in terms of n individual weighting factors associated with respective ones of said n joints, said weighting factors determining the joints for which gravity loading is minimized.
Claim 5
Independent Claim
162 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to a minimization of joint inertia on said joints, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of a joint inertia function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said minimization of joint inertia.
Claim 6
Independent Claim
162 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to a minimization of joint inertia on said joints, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of a joint inertia function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said minimization of joint inertia.
Claim 7
Dependent Claim
47 words
The method of claim 4 wherein said joint inertia function is a function of the angles of all of said n joints and comprises a sum over all of said n joints of off-diagonal joint-coupling elements of a joint inertia matrix for each one of said joints.
Claim 8
Independent Claim
171 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to an optimization of joint mechanical advantage of said joints, wherein said second defining comprises, defining an n-by-r matrix opertor, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of a joint mechanical advantage function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition whereby to minimize joint mechanical advantage; and controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said optimization of joint mechanical advantage.
Claim 9
Independent Claim
171 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to an optimization of joint mechanical advantage of said joints, wherein said second defining comprises, defining an n-by-r matrix opertor, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of a joint mechanical advantage function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition whereby to minimize joint mechanical advantage; and controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said optimization of joint mechanical advantage.
Claim 10
Dependent Claim
51 words
The method of claim 6 wherein said joint mechanical advantage function is a function of the angles of said joints and comprises a projection of an end effector Jacobian matrix of a respective joint and a unit vector of a direction of applied force of an end effector for each joint.
Claim 11
Independent Claim
170 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to an optimization of an end effector-to-joint angle velocity ratio, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of an end effector-to-joint angle velocity ratio function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and, controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said optimization of an end effector-to-joint angle velocity ratio.
Claim 12
Independent Claim
170 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to an optimization of an end effector-to-joint angle velocity ratio, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of an end effector-to-joint angle velocity ratio function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and, controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said optimization of an end effector-to-joint angle velocity ratio.
Claim 13
Dependent Claim
31 words
The method of claim 8 wherein said end effector-to-joint angle velocity ratio function comprises projections of end effector Jacobian matrices of respective joints and an angular velocity vector of respective joints.
Claim 14
Independent Claim
164 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to optimization of end effector movement sensitivity, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of an end effector movement sensitivity function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and, controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said optimization of end effector movement sensitivity.
Claim 15
Independent Claim
164 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to optimization of end effector movement sensitivity, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of an end effector movement sensitivity function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and, controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said optimization of end effector movement sensitivity.
Claim 16
Dependent Claim
27 words
The method of claim 10 wherein said end effector movement sensitivity function comprises a trace of a product of an end effector Jacobian matrix with its transpose.
Claim 17
Independent Claim
162 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to optimization of end effector compliance, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of an end effector movement compliance function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and, controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said optimization of end effector compliance.
Claim 18
Independent Claim
162 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to optimization of end effector compliance, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of an end effector movement compliance function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and, controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said optimization of end effector compliance.
Claim 19
Dependent Claim
33 words
The method of claim 12 wherein said end effector compliance function comprises a sum of squares of matrix elements of a projection of an end effector Jacobian matrix on a joint stiffness matrix.
Claim 20
Independent Claim
164 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to optimization of end effector impact force, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of an end effector impact force function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and, controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said optimization of end effector impact force.
Claim 21
Independent Claim
164 words
A method of controlling a redundant robot having n joints operating in m-dimensional task space with redundancy r=n-m, and having an end effector, said method comprising: first defining a basic task motion of said robot within a set of end-effector coordinates, corresponding to m constraints on movement of said n joints; second defining not more than r constraints on said basic task motion corresponding to optimization of end effector impact force, wherein said second defining comprises, defining an n-by-r matrix operator, N e , spanning a null space of a Jacobian operator of said end-effector, defining an n-by-1 vector which is a partial derivative of an end effector impact force function with respect to angles of said joints, and setting the product of said matrix operator and said vector to zero as a minimization condition; and, controlling said joints so as to simultaneously fulfill the m constraints of said basic task motion and the r constraints of said optimization of end effector impact force.
Claim 22
Dependent Claim
33 words
The method of claim 14 wherein said end effector impact force function comprises a projection of an end effector mass matrix on a unit vector of an impact force of an end effector.
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