Benefiting From Kinematic Redundancy Alongside Mono- and Biarticular Parallel Compliances for Energy Efficiency in Cyclic Tasks

In this paper, we answer two interleaved questions. The first one is, having a redundant serial manipulator with a given cyclic task, how can we benefit simultaneously from both natural dynamics modification (NDM) and kinematic redundancy resolution to reduce the actuators' torque? Here, the NDM is done by devising parallel nonlinear monoarticular compliances (MACs), which span one joint, and nonlinear biarticular compliances (BACs), which pass over two joints. We take advantage of kinematic redundancy to exploit the robot's natural dynamics. The second question is how do kinematic redundancy resolution and the NDM interact to minimize the cost? To answer these questions, we cast the problem of simultaneous modification and exploitation of natural dynamics into a constrained multiobjective optimization problem. We show that the set of optimal compliances has an analytical solution as a parametric function of joint trajectories. Accordingly, we study how the components of cost function affect the profile of optimal compliant elements. The proposed method is implemented on a simulated planar 3-DoF manipulator and a simulated nonplanar 4-DoF manipulator for three different tasks. The results shed light on how kinematic redundancy resolution influences efficiency of using MACs and BACs and, consequently, increases attainable gains from the NDM. Moreover, analysis of the results specifies the roles of mono- and BACs and especially explains the reason behind the particular importance of having BACs to reduce the actuation cost.