Abstract
In this paper, we introduce a numerical optimal control scheme (NOCS) for generating dynamically feasible robot motions under several constraints while optimizing a given performance criterion. In particular, the NOCS transforms continuous optimal control problems into large-scale sparsity-free nonlinear programs (NLPs) by means of a dedicated strategy called the block indexation procedure (BIP). As a result, the optimized open-loop control law is obtained fast under limited-memory allocation. The robot’s equations of motion, and their partial derivatives with respect to the state of the robot and control inputs, are analytically evaluated. For this, state-of-the-art algorithms available in the Pinocchio and RBDL open-source libraries are used. Otherwise, the NOCS applies the BIP with numerical differentiation techniques. The effectiveness of the NOCS is numerically validated with different robots composed by many degrees of freedom. Also, we provide performance comparisons against CasADi, a popular general purpose optimal control framework that applies automatic differentiation.