Towards Unified Framework for Trajectory Optimization Using General Differential Kinematics and Dynamics

Abstract

This paper presents a new framework for trajectory optimization using comprehensive differential kinematics and dynamics theory, and also its applications and perspectives. For a robotic system with large degrees of freedom including humanoid robots, numerical gradient computation is not practical in terms of precision and time. Trajectory optimization is more and more demanded in different fields not only for usual motion planning but also motion imitation, dynamic parameter identification and human motion understanding. The proposed theory is based on the comprehensive motion transformation matrix (CMTM) that allows describing variational relationship in differential kinematics and dynamics including velocity and acceleration based on a simple chain product. This enables analytical gradient computation of various physical quantities such as joint force or torque with respect to trajectory parameters, which is beneficial to various optimization problems. We overview the possible evolution brought by this technique and demonstrate its advantages through examples of efficient optimization of dynamic motions for a redundant robot and a humanoid under severe constraints. Also, we discuss the possibility of its integration in optimal control method.