Towards Minimal Intervention Control with Competing Constraints

As many imitation learning algorithms focus on pure trajectory generation in either Cartesian space or joint space, the problem of considering competing trajectory constraints from both spaces still presents several challenges. In particular, when perturbations are applied to the robot, the underlying controller should take into account the importance of each space for the task execution, and compute the control effort accordingly. However, no such controller formulation exists. In this paper, we provide a minimal intervention control strategy that simultaneously addresses the problems of optimal control and competing constraints between Cartesian and joint spaces. In light of the inconsistency between Cartesian and joint constraints, we exploit the robot null space from an information-theory perspective so as to reduce the corresponding conflict. An optimal solution to the aforementioned controller is derived and furthermore a connection to the classical finite horizon linear quadratic regulator (LQR) is provided. Finally, a writing task in a simulated robot verifies the effectiveness of our approach.