Optimal filters from task velocities to joint velocities including both position and velocity limits

To implement extremely precise motion control over a very wide positional range and bandwidth, several actuators with different characteristics are often needed (e.g. coarse, fine, very fine). Often it is not clear how a desired task space trajectory should be divided among the actuators, especially when the actuators are connected together by complex kinematics. For instance, parallel linear actuators are often used to produce rotational motion because the parallel configuration provides high stiffness to weight, fault tolerance, etc. A new, general method for dividing a desired task space velocity among redundant actuators with complementary position and velocity limits has been found. Novel aspects of the approach are: (1) Any number of joint space actuators with many different position and velocity characteristics can be included; (2) Any number of output (task) velocities can also be included; (3) The method yields a transfer matrix mapping task velocities to joint space velocities, thus it is easily implemented (e.g. it does not require measurement of joint position, etc.). This method has been applied to pointing by connecting a precision Stewart platform and a fast steering mirror in series, thus creating a system capable of pointing very precisely over large positions and bandwidths in a fault tolerant manner. Experimental results show a factor of four reduction in pointing errors.