Trajectory Optimization of Flexible Robots Using an Optimal Control Approach

In the context of the mechatronic design of lightweight machines and robots, this paper studies optimal control problems in flexible multibody dynamics. Based on a direct transcription of the initial problem, a direct collocation method is used. This method leads to a large but sparse nonlinear programming problem for which standard solvers are available. The implemention of this method based on a finite element simulation tool for flexible multibody systems is described. The connections between the generalized-alpha time integration scheme, which is commonly used for this kind of applications, and the formulation of the optimization problem are highlighted. The methodology is illustrated for two academic examples of rigid and flexible robotic systems.