Constrained Near-Optimal Control using a Numerical Kinetic Solver

A.L. Jennings, R. Ordóñez, and F.G. Harmon (USA)


Optimal control, Computer Aided Design, Numeric methods, Nonlinear, Robotics


Optimal control problems are challenging to solve even on simple systems. Few problems afford analytical solutions because of the boundary valued differential equations. Ki netic systems, such as robotic linkages, can be complicated to solve because of nonlinearities and degrees-of-freedom. A numeric control optimization software, DIDO, is cou pled to a numeric kinetic solver, SimMechanics, within MATLAB. The kinetic model is created directly from a solid model assembly eliminating human errors. A pen dulum with control saturation is tested to validate satisfac tion of theoretical conditions (< 10% optimality residu als, 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 pick and-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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