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Optimal controller applied to robotic systems using covariant control equations

ABSTRACT We elaborate an algorithm to optimally control the actuators of robot manipulators. By regarding the robot kinetic energy as a metric, the dynamic model is formulated using tensors in a Riemannian geometry manifold. The control criterion is selected to be invariant, leading to covariant control equations that take advantage of the system dynamics. Motion equations are associated with conjugate control equations resulting in a system of second order ordinary differential equations. The suggested control method consists in solving this system of equations to obtain optimal joint forces off-line and use them as inputs in a control scheme to track optimal trajectories. Position-velocity feedback ensures proper behaviour. Motion control simulations show that the optimal trajectory can be tracked with good accuracy, even with imposed perturbations. A stability analysis for switched systems precedes real-time motion control experiments conducted on a serial robot manipulator with revolute joints to validate our method.