Optimal control for Simplified Model of Human Arm by Using Bang-Bang Technique

Abstract

Recently, intrinsic compliant actuation is not considered the clear drawback in robotics, whereas it is widely recognized as advantageous to robot control once dynamic task is consider. However, the benefit of intrinsic compliance comes with high control complexity. Specifically, it is not easy ad non-trivial if coordinating the motion of a system through a compliant actuator and finding a task-specific impedance profile that leads to better performance. Here, I propose an optimal control which is a combination of the bang-bang control and Nelder-Mead algorithm to compute the motor position commands, and the associated time-varying torque and stiffness profiles. To demonstrate the utility of the approach, I consider an “explosive” ball-throwing task where exploitation of the intrinsic dynamics of the compliantly actuated system leads to improved task performance (i.e distance thrown). In this example I show that: (i) the proposed control methodology is able to tailor impedance strategies to specific task objectives and system dynamics, (ii) the ability to vary stiffness can be exploited to achieve the better performance, (iii) in system with variable physical compliance, the present formulation enables exploitation of the energy storage capabilities of the actuators to improve task performance. I illustrate these in numerical simulation of a two-link and three-link variable stiffness robots.