Actuation Optimization of Tensegrity Robotics Based on Minimization of Input Energy

The six-strut spherical tensegrity robot (TR-6), known for its lightweight, high robustness, and adaptability, demonstrates superior kinematic performance due to its significant structural deformability. Its symmetric geometry is well suited for rolling locomotion, enabling the robot to adapt to changing terrain, navigate unstructured environments, and perform missions even after suffering massive damage. This article investigates the minimization of actuation cost for tumbling motion in TR-6 by employing a hybrid optimization framework based on the beetle antennae-genetic algorithm. To this end, an energy-efficient propelling model is formulated, in which strain energy discrepancy is adopted as the objective function, and constraints such as gravitational moment, strain energy limit, and cable regulation bounds are incorporated. The nonrigid-body motion analysis method is applied to determine the robot's equilibrium posture under unbalanced forces. The proposed approach is validated through multibody dynamic simulation using the ADAMS software and further confirmed by physical prototype experiments with motor-driven TR-6 hardware. Results demonstrate that the proposed method effectively identifies actuation strategies with reduced energy consumption and can be extended to other multi-strut or strut-actuated tensegrity robotics.