Auto-Tuning of Controller and Online Trajectory Planner for Legged Robots

This letter presents an approach for auto-tuning feedback controllers and online trajectory planners to achieve robust locomotion of a legged robot. The auto-tuning approach uses an Unscented Kalman Filter (UKF) formulation, which adapts/calibrates control parameters online using a recursive implementation. In particular, this letter shows how to use the auto-tuning approach to calibrate cost function weights of a Model Predictive Control (MPC) stance controller and feedback gains of a swing controller for a quadruped robot. Furthermore, this letter extends the auto-tuning approach to calibrating parameters of an online trajectory planner, where the height of a swing leg and the robot’s walking speed are optimized, while minimizing its energy consumption and foot slippage. This allows us to generate stable reference trajectories online and in real time. Results using a high-fidelity Unitree A1 robot simulator in Gazebo provided by the robot manufacturer show the advantages of using auto-tuning for calibrating feedback controllers and for computing reference trajectories online for reduced development time and improved tracking performance.

I. Introduction

Planning and control of legged systems is challenging due to the tight coupling of reaction forces generated by foot contacts with the environment and the motion of the robot’s base. This problem is further complicated as legged systems for real-world deployment are expected to traverse highly unstructured environments such as debris, obstacles, and rough terrain. Traditional control designs such as those employing Raibert or heuristic controllers [1] can only guarantee physical feasibility on smooth or flat surfaces. Optimization-based approaches often use a cost function to account for kinematic, dynamic, and friction-cone constraints. E.g., the Linear Inverted Pendulum approach optimizes over the Center of Mass (CoM) position, where the footsteps must be specified a priori to satisfy the Zero-Moment Point [2]. This approach has some drawbacks because pre-defining the footholds’ locations on the ground may restrict the robot’s range of achievable motion. Further, whole-body controllers that do not require pre-defined footholds, e.g., in [3], may be sub-optimal as they only consider the current joint torques.