Operational Space Balancing Control Based on Integrated CoM Dynamics for Underactuated Triple Pendulum Robot

This letter introduces a novel control method for the underactuated triple pendulum robot (UTPR), allowing it to maintain balance while controlling the end-effector motion in the operational space. The UTPR is influenced by gravity in the vertical plane, with the first joint being passive (underactuated) and the rest being active (actuated). Previous research primarily focused on controlling end-effector motion within a gravity-free plane or investigating pendulum swing-up motion under gravity's influence. This letter proposes a novel dynamic model that includes the dynamics of the center of mass (CoM) and the operational space, describing the exact balancing physical processes of the system. Based on the new dynamic model and analysis of its inherent constraints, we derive the relationship between angular momentum and the CoM and design an effective operational space and balancing controller. Due to underactuation, a Quadratic Programming (QP) based controller is devised to minimize the error between the desired acceleration commands and actual accelerations. Simulation results demonstrate that the proposed method enables the system's end-effector to maintain stability at the task point and under external force disturbance and achieves excellent trajectory tracking.