Optimal control of an ISS-based robotic manipulator with path constraints

Optimal path-constrained trajectories of an ISS-based, three-link robot are investigated with a monorail as an additional fourth and prismatic joint. This results in a problem of optimal control for a multiple constrained nonlinear system of differential-algebraic equations. After transformation into minimum coordinates, the only remaining control is the acceleration of the end-effector along the prescribed trajectory, replacing four actuator torques/forces in the original formulation. The simpler structure is achieved at the price of introducing piecewise defined equations of motion, two highly nonlinear control constraints and two state constraints of first order. Switching points between partly linear and fully rotational motion are optimized. Solutions are presented including touch points of the state constraints with the two control constraints being active simultaneously. For the mathematical treatment of those problems, new interior point conditions are derived.