A Unified Trajectory Optimization Approach for Long-Term and Reactive Motion Planning of Legged Locomotion

This paper proposes a unified trajectory optimization approach that simultaneously optimizes the trajectory of the center of mass and footholds for legged locomotion. Based on a generic point-mass model, the approach is formulated as a nonlinear optimization problem, incorporating constraints such as robot kinematics, dynamics, ground reaction forces, obstacles, and target location. The unified optimization approach can be applied to both long-term motion planning and the reactive online planning through the use of model predictive control, and it incorporates vector field guidance to converge to the long-term planned motion. The effectiveness of the approach is demonstrated through simulations and physical experiments, showing its ability to generate a variety of walking and jumping gaits, as well as transitions between them, and to perform reactive walking in obstructed environments.