Projected inverse dynamics control and optimal control for robots in contact with the environment: A comparison

This paper addresses the problem of constrained motion for a manipulator performing a task while in contact with the environment, and investigates two force control frameworks, one based on projected inverse dynamics, and one based on optimal control. Firstly, we propose a control method based on projected inverse dynamics, which directly exploits the contact constraints to minimise the instantaneous joint torques needed to perform a task. Secondly, we propose an optimal control strategy which provides a tool to minimise the joint torques over an interval of time. We show how contact constraints can be used as optimisation constraints in the definition of the problem, and how to formulate the optimal control problem directly using projected dynamics. Initially we explore a positional control problem, where the robot is required to follow a desired path, and show that both of the proposed methods can satisfy the positional task while significantly reducing the joint torques as compared to simple kinematic control and also classical inverse dynamics control. We also show that the proposed optimal control method outperforms the pure projected inverse dynamics method in terms of minimising the required joint torques. We then show how each method can be extended to follow a desired path while also exerting a desired contact force. Again, the method incorporating optimal control is shown to satisfy the task requirements with significantly smaller commanded torques than the pure projected inverse dynamics method. To confirm the analysis, and demonstrate proof of concept, we present the results of empirical experiments with a simulated 3-degree-of-freedom planar manipulator which is constrained to move while in contact with a rigid surface.