EXECUTIVE SUMMARY
FINAL REPORT FOR NASA9-19272,
NATURAL TRACKING CONTROL FOR TELEROBOTIC SERVICING ROBOTS

M & M TECHNOLOGIES, INC., P.O. BOX 399, LEXINGTON, SC 29071-0399
June 13, 1995

In Phase I research, Natural Tracking Control (NTC) for multi degree-of-freedom (DOF) non-redundant and redundant robots controlled in Cartesian space forced prespecified elementwise exponential tracking of time varying desired outputs while compensating for unknown internal dynamics and external disturbances. In Phase I, NTC algorithms successfully controlled through simulation two and three DOF robots subjected to external nonlinear, unknown pulse, random torque disturbances and internal backlash and friction disturbances.

Natural tracking control of Cartesian space robots for Phase I was demonstrated with three distinct, nonlinear robot models. The robots were modeled as rigid bodies operating in Cartesian space. The models included inertial, Coriolis, centrifugal and gravity forces. One robot model was of a two degree-of-freedom (DOF) manipulator with two revolute joints (RR) which operated in the U² Cartesian (xz) vertical plane. Another robot model was a three DOF manipulator with three revolute joints (RRR) which operated in U³ Cartesian space (xyz), similar to the space shuttle manipulator arm SRMS. In addition, a three DOF planar redundant robot was modeled and simulated which operated in U² Cartesian plane space, i.e. the three independent joints moving in a plane gave multiple solution possibilities for the position of the end effector. All of these robots were controlled in Cartesian space with the same basic natural tracking control algorithm.

Phase I natural tracking control simulations also demonstrated pre-specified elementwise exponential tracking; i.e. the elementwise vector difference between the time varying desired output and the real output. In the simulations for these robots, whether redundant or not, several different exponential tracking error "qualities" were demonstrated and reported. The prespecified tracking quality can be selected by the designer (operator) based upon the desired convergence of the tracking error, not the dynamics of the robot; natural tracking control separates the tracking error convergence and the individual control of each Cartesian output. Different integration methods and step sizes were also investigated for their effects on stability and smoothness of the tracking error.

The robot models were subjected to internal nonlinearities and external disturbances; these include backlash in the actuator path, band-pass limited white noise torque disturbances, and frictional torque. The backlash in the actuator path was increased two-orders of magnitude well beyond that encountered in geared applications and hunting was not observed for constant desired outputs. Band-pass limited white noise torque disturbances were completely compensated while following time varying desired outputs. Static and dynamic friction torque were successfully modeled, simulated and compensated for by natural tracking control. NTC compensated these disturbance and nonlinearities without any knowledge of their form or value.

The proposed objectives in Phase II are: extensions of NTC to the rigid body six DOF NASA SRMS. model; experimental real-time verification with single and multi-link robots; parallelizing NTC algorithms; and real-time commercial controller specification. Phase II planned activities include establishing closer cooperative ties with NASA/JSC by the SRMS. simulation; establishment of a real-time experimental laboratory and construction of controlled robots; the establishment of parallel computation capabilities; and the expansion of cooperative ventures for commercialization of NTC robot controllers. The anticipated Phase II results are the demonstration of NTC for six DOF robots by simulation; the real-time verification of NTC algorithms; explicit formulation of parallel NTC algorithms; and specification of a general-purpose natural tracking controller.