Quadrupedal robots are highly regarded for their superior locomotion capabilities and terrain adaptability, making them competent in a wide range of applications. In autonomous navigation tasks, they are required to track upper-level trajectories to reach designated locations with flexible obstacle avoidance. This is typically achieved by a planner which generates a reference velocity and a controller which accurately tracks the velocity commands. In this article, we propose a learning-based controller for quadrupedal robots that achieves accurate and robust velocity tracking. To bridge the gap between simulation and reality, an analytical actuator model is proposed to simulate physical actuator dynamics. We then train a control policy in simulation using Constrained Reinforcement Learning, where symmetry and smoothness constraints are incorporated into reinforcement learning. The symmetry constraint promotes coordinated locomotion and consistent velocity tracking performance, while the smoothness constraint reduces jerky actions and generates stable velocity performance. The control policy is zero-shot deployed on the Unitree AlienGo. It demonstrates a tracking error of less than 0.084 m/s over the entire velocity range and robust locomotion on natural terrain. We also test our controller by integrating it to a pedestrian tracking framework and prove its capability of trajectory following and long-term reliablitiy.
