Torque minimisation of the 2-DOF serial manipulators based on minimum energy consideration and optimum mass redistribution

This paper deals with the analytically tractable solution for input torques minimisation of two degrees of freedom serial manipulators based on minimum energy control and optimal redistribution of movable masses. The minimisation problem is carried out in two steps: at first, the optimal trajectory of the manipulator is defined as a function, which leads to the minimisation of energy consumption. Then, by introducing the obtained trajectory into dynamic equations, the torques are reduced by using the optimal redistribution of movable masses, which is carried out via an adaptive counterweight system. For this purpose, the torques due to the dynamic loads of the counterweights are presented as a function of the counterweight positions. The conditions for optimal dynamic balancing are formulated by minimisation of the root-mean-square value of the input torque including the dynamic loads of the unbalanced manipulator and counterweights. The suggested approach is illustrated by numerical simulations carried out using ADAMS software.