Reinforcement Learning for Bipedal Jumping: Integrating Actuator Limits and Coupled Tendon Dynamics

In high-dynamic bipedal locomotion control, robotic systems are often constrained by motor torque limitations, particularly during explosive tasks such as jumping. One of the key challenges in reinforcement learning lies in bridging the sim-to-real gap, which mainly stems from both inaccuracies in simulation models and the limitations of motor torque output, ultimately leading to the failure of deploying learned policies in real-world systems. Traditional RL methods usually focus on peak torque limits but ignore that motor torque changes with speed. By only limiting peak torque, they prevent the torque from adjusting dynamically based on velocity, which can reduce the system’s efficiency and performance in high-speed tasks. To address these issues, this paper proposes a reinforcement learning jump-control framework tailored for tendon-driven bipedal robots, which integrates dynamic torque boundary constraints and torque error-compensation modeling. First, we developed a torque transmission coefficient model based on the tendon-driven mechanism, taking into account tendon elasticity and motor-control errors, which significantly improves the modeling accuracy. Building on this, we derived a dynamic joint torque limit that adapts to joint velocity, and designed a torque-aware reward function within the reinforcement learning environment, aimed at encouraging the policy to implicitly learn and comply with physical constraints during training, effectively bridging the gap between simulation and real-world performance. Hardware experimental results demonstrate that the proposed method effectively satisfies actuator safety limits while achieving more efficient and stable jumping behavior. This work provides a general and scalable modeling and control framework for learning high-dynamic bipedal motion under complex physical constraints.