Model-Based Control Implementation of Quadruped Robots with MuJoCo

Control algorithms rely on robot simulation platforms to evaluate the dynamics of the controlled robot. For legged robot simulators, the ability to handle contact and friction is fundamental. Many robot simulation platforms are designed for virtual prototyping, replicating the kinematics, dynamics, and real-world interactions of robotic systems. Among these, MuJoCo stands out. Despite the widespread use of MuJoCo in the literature, there is a lack of detailed documentation on the settings required for implementing model-based control techniques. Here, we present the implementation of inverse dynamics impedance control within a locomotion control framework based on compliant foot trajectory tracking. We provide the theoretical foundation for defining the system model and control scheme, and explain how to extract the corresponding terms from MuJoCo. The settings for contact parameters and the calculation of contact forces are detailed, with each linked to its corresponding theory. To illustrate MuJoCo’s practicality, we present an application featuring a quadruped robot modeled on the MIT Mini Cheetah. We analyze and simulate the effects of contact parameters on the dynamics of the controlled robot. Finally, videos showcase simulations of the controlled quadruped robot, highlighting the effects of varying contact parameter values on contact dynamics.