Trajectory control and obstacle avoidance for robot manipulators with bounded inputs
Jeffrey Marc Kleinwaks · 1985
The dynamic equations for a robot manipulator are generally represented by coupled, non-linear state equations. A non-linear controller is developed in this thesis that considers the complete non-linear system dynamics. In addition, the control allows for bounds on the system inputs, such as limited input torque from the joint motors. The control is based upon the application of an Optimal Decision Strategy, a pointwise optimization process. This results in the design of the control being reduced to the solution of a quadratic programming problem at each sample point. The robustness of the control scheme to unmodeled dynamics is examined and a robust control is presented. A real-time implementation of this control is developed for a three degree of freedom robot manipulator. The control is implemented using 16 bit microprocessor and is programmed in a high level language. The manipulator dynamics are computed using the Euler-Lagrange formulation and the control system is run with a sample period of 16 milliseconds. A path planning strategy for a two degree of freedom Cartesian manipulator with obstacles in the workspace is developed. Previous path planning strategies have usually neglected manipulator dynamics, with the potential result of a trajectory that cannot be followed by the manipulator. The concept of an extended obstacle is presented where the obstacle is defined in both position and velocity space. This allows for the consideration of bounded inputs in the obstacle avoidance strategy. A control is computed based upon the Optimal Decision Strategy, and then examined to see if the resulting trajectory hits the extended obstacle. If so, an avoidance control is then applied. The obstacle avoidance strategy results in a trajectory that can always be tracked by the manipulator, and has the potential to be implemented on-line.