A computational strategy for trajectory optimization of underactuated multibody systems with contacts

In this paper we propose a strategy for improving the computational efficiency of direct methods for trajectory optimization of multibody systems. We particularly focus on those applications where the system necessarily has to interact with the surrounding environment through intermittent contacts. The problem is hereby formulated such that just the initial and final states of the system over a given time interval are prescribed, so as to let the solver automatically synthesize the best contact sequence to accomplish the considered task. The proposed computational strategy consists in: (i) solving a preliminary optimization problem that roughly approximates the original one, but differs from it by one or more conveniently chosen parameters and is faster to solve; (ii) using the obtained solution as an initial guess for the actual (full-fledged) optimal control problem. The performance of the method is evaluated in a simulated planar system, whose peculiarity is to be trivially underactuated. An extensive investigation is presented which shows how a proper choice of the parameters in the preliminary optimization can lead to a significant reduction in the computational effort required to solve the problem. The results we present assess both the validity and the robustness of the proposed method.