Techniques for real-time simulation of robot manipulators.

Abstract

The subject of this thesis is the efficient numerical modeling of multiple degree-of-freedom (DOF) robot manipulators. At the outset an efficient exact rigid-body model of a 6 DOF robot with a digital controller is formulated using the Newton-Euler (N-E) and Orin-Walker algorithms, controlled by the computed-torque method. Execution of a single pass through this model on the AD-100 computer, a 20 MFLOPS multiprocessor, requires 275 microseconds, while the st and ard N-E computations execute in 96 microseconds. This performance supports simulation of 6 DOF robot dynamics at more than 14 times faster than real time. The mixed-data nature of the simulated robot system has motivated the development of two hybrid integration methods. These methods combine the self-starting feature of the Runge-Kutta (RK) algorithms with the computational efficiency of the modified single-pass Adams-Moulton (SPAM) methods. It is shown through example problems, including a 6 DOF robot simulation, that a method based on Gear's 3rd-order start-up and the SPAM-3 algorithm consistently outperforms, in speed or accuracy but not stability, the RK-3 algorithm. An efficient actuator model with effort limiting is also developed. This model necessitates the solution of stiff ODEs by discretizing the actuator relations and analytically solving the resultant linear equations. Actuator limiting is accommodated by merging the proportional and saturated solutions at appropriate points. Although computationally involved, this procedure is shown to retain high accuracy even when executed in faster than real time. Also described is a faster than real-time Coulomb friction model that preserves the dependence of friction on normal forces. This fixed-step model operates by retroactively correcting for the friction discontinuities. Its implementation requires the solution of an implicit equation in the joint accelerations. This solution is performed iteratively and furnishes accurate results into passes, making possible simulation of 6 DOF robot dynamics with actuator and friction effects at close to 3 times faster than real time. Included in this work are extensive simulation results that illustrate the impact of these enhancements on the model accuracy and on the simulated robot performance. Also provided is a breakdown of the execution times and maximum allowable integration step sizes.