Trajectories generation for robot manipulators under constraints including compliance and robust friction model in interaction with external dynamics

Robots are always on interaction with their environment, for example a robot manipulator with its load, a robot machine tool with its task. We present in this article a semi-analytical method for trajectory synthesis of robot manipulators involved by the static or dynamic state feedback linearization and decoupling method, under multiple nonlinear dynamical constraints including compliance, robust friction model and interaction with other dynamics. The aim of this method is to use the known analytical nonlinear mappings which relates respectively, the set of the linear admissible control vectors, the set of the admissible outputs, the set of the admissible nonlinear state vectors and the set of the admissible non linear control vectors, to overcome the numerical integration problem and to transpose it in an optimal problem of an exact algebraic functional. This method which discards the numerical problem of stability and convergence of the solution is particularly useful for large nonlinear systems for example, the control of the full nonlinear dynamics of robot manipulators.