Zero-power balancing a two-link robot manipulator for a predefined point-to-point task

Abstract

In this paper, a new balancing approach called “zero-power balancing” (ZPB) method is presented for a two-link robot manipulator (TLRM) whose end-effector must move on a vertical plane between two given points repeatedly. To this purpose, a simple balancing mechanism which has two adjustable degrees of freedom is presented by which the required power will be zero and the proposed method can be applied for any specific boundary conditions. In order to solve the problem, balancing problem is formulated as an optimal control problem on which the required optimality conditions were derived using the Pontryagin’s minimum principle, leading to a two-point boundary value problem (TPBVP). By solving the obtained TPBVP, states, controls and the constant parameters of the counterweights were simultaneously determined. By considering the performance index as minimum effort, it was interestingly observed that the values of torque at joints vanished perfectly and identical counterweight’s specifications were obtained in forward and return motions, so that the manipulator could swing between the two given points freely. Capability of the proposed method to implement the swinging motion between the two desired points was illustrated via simulation. Due to friction, air resistance, and parametric uncertainties, it was practically difficult to implement the motion repeatedly and at no power consumption as an open-loop policy, but rather two small actuators are required to control the manipulator along the optimal trajectory. Finally, an experimental set-up was developed to validate the simulation results and illustrated the efficiency of the ZPB method.