NASA's Jet Propulsion Laboratory,Pasadena, California
A method for the control of a robot arm is based on computed nonlinear feedback and state transformations to linearize the system and decouple the robot end-effector motions along each of the Cartesian axes in the workspace. The nonlinear feedback is augmented with an optimal scheme for the correction of errors in the workspace. The mathematical model of the robot arm is stated in homogeneous coordinates together with the Denavit- Hartenberg four parameter representation of robot-arm kinematics. Using the Lagrangian formulation of mechanics, the dynamic behavior of the robot arm is expressed in matrix/vector form and manipulated to obtain expressions of the types previously found useful in nonlinear-control theory. The resulting dynamic-control mathematical model satisfies the necessary and sufficient conditions for external (or exact) linearization and simultaneous output decoupling. By using non-linear feedback and a diffeomorphic transformation, the non- linear system of dynamical equations is converted into a Brunovsky canonical form and simultaneously output- decoupled. The linearization accomplished here by non-linear feedback is an "external linearization" as opposed to the conventional "internal linearization" (Taylor-series expansion). That is, the nonlinear character of the original system is not changed here by any approximation. Therefore, system linearization by nonlinear feedback can be called "exact linearization" in a control sense. The linearized system is unstable. To stabilize it, a linear feedback loop is added. As long as the feedback matrix is constant and block-diagonal, the system will remain an output-decoupled linear system. A major new feature of the control method is that the optimal error- correction loop directly operates on the task level and not on the joint-servo- control level. The task-level errors are then decomposed by the nonlinear-gain matrix into joint-force or joint-torque-drive commands. The new control method performed well in computer simulations. The augmentation of non-linear feedback with an optimal error-correcting control provides robust performance and assures acceptable tracking errors even when the dynamical parameters of the mathematical model of the robot arm are in error by as much as 30 percent.
Point of Contact:
Antal K. Bejczy
Mail Stop 198-219
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena CA 91109
818-354-4568
bejczy@telerobotics.jpl.nasa.gov
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Maintained by: Dave Lavery
Last updated: May 10, 1996