Kinematic functions for redundancy resolution using configuration control

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.sub.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.

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.sub.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.

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.sub.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.

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.sub.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.

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.sub.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.

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.sub.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.