Autonomous and Safety-Critical Stair Climbing via Nonlinear Model Predictive Control for Quadrupedal Robots

Motion planning for quadrupedal robots on unstructured terrains demands the consideration of torso terrain adaptation and safety foothold placement. This paper presents an autonomous and safety stair climbing control strategy, aiming to simultaneously optimize body and leg movements. An improved mobility metric taking into account leg mobility and maintaining stability margin, is introduced. By penalizing deviations from the current joint angle and nominal leg configuration in the cost function, the stance legs can naturally extend to lifting body, and the projection of the center of mass is always inside the support region. Then, the reference climbing velocity is automatically determined based on the geometric information of the stairs. With these reference velocities, we solve a two-layer control framework which couples nonlinear model predictive control (MPC) with whole-body control (WBC), and add several different control barrier functions (CBF) constraints to ensure safety foot placement and edge avoidance. Note that each constrained act on the kinematics or dynamics level depends on the order of the system dynamics. In the simulation, we demonstrate that the robot efficiently climbs several different size stairs with 10 cm height (25% of the maximum leg length) and the maximum climbing velocity reaches 0.64m/s.