This paper presents a tracking controller considering contact force constraints for floating-base humanoid robots. The goal of the tracking controller is to compute the joint torques such that the robot can imitate given reference motions obtained from, for example, human motion capture data. The technical challenge is that the robot motion depends not only on joint torques but also on contact forces from the environment, which depend on the joint torques and are subject to constraints on friction forces. Therefore, computing the joint torques and associated contact forces typically results in a nonlinear optimization problem with complex constraints. We solve this issue by taking advantage of the property that the motion of the floating base is only affected by contact forces. We can then compute the contact forces and joint torques separately by solving two simple sequential optimization problems. Through dynamics simulations, we demonstrate that the proposed tracking controller successfully enables a humanoid robot to reproduce different human motions, including those with contact state changes.
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