A Method for Trajectory Optimization of Robots having Contacts or Motion Constraints

The problem of motion trajectory optimization with constraints is considered for robotic system with actuated joints. Constraints concern contacts and path-following in the Cartesian space. These constraints arise in walking patterns. In this study, we are dealing with cases where the same constraints hold during a given motion. The trajectory optimization is performed by defining some state variables as polynomials, and the best parameters of the polynomial functions are obtained from suitable optimization programs. By taking into account motion constraints, it appears that the number of the problem's optimization parameters can be reduced. Subsequently, the structure of the optimization problem is different. A procedure to solve this optimization problem is proposed. A simple case is used to compare the proposed methods with the one that is used for solving the similar problem without parameters reduction