Constrained Near-Optimal Control Using a Numerical Kinetic Solver

Optimal control problems are challenging to solve even on simple systems. Few problems afford analytical solutions because of the boundary valued differential equations. Kinetic systems, such as robotic linkages, can be complicated to solve because of nonlinearities and degrees-of-freedom. A numeric control optimization software, DIDO, is coupled to a numeric kinetic solver, SimMechanics, within MATLAB. The kinetic model is created directly from a solid model assembly eliminating human errors. A pendulum with control saturation is tested to validate satisfaction of theoretical conditions (< 10% optimality residuals, typically < 5%). The numeric method is contrasted to a linear-quadratic-regulator (LQR) and the optimal linear state transfer. A four degree-of-freedom, arm robot pickand-place command is also optimized and realizes a 50% decrease in energy used over a ramp to constant velocity maneuver. This coupling obtains near optimal solutions without intense, model specific analysis.

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