Centroidal-momentum-based trajectory generation for legged locomotion

This paper presents a trajectory optimization framework for planning dynamic legged locomotion based on a robot’s centroidal momentum (CM), which is the aggregation of all the links’ momenta at the robot’s Center of Mass (CoM). This new framework is built around CM dynamic model driven by Ground Reaction Forces (GRFs) parameterized with Bézier polynomials. Due to the simple form of CM dynamics, the closed-form solution of the robot’s CM can be obtained by directly integrating the Bézier polynomials of GRFs. The CM can be also calculated from the robot’s generalized coordinates and velocities using Centroidal Momentum Matrices (CMM). For dynamically feasible motions, these CM values should match, thereby providing equality constraints for the proposed trajectory optimization framework. Direct collocation methods are utilized to obtain feasible GRFs and joint trajectories simultaneously under kinematic and dynamic constraint. With the closed-form solutions of CM due to the parameterization of GRFs in the formulation, numerical error induced by collocation methods in the solution of trajectory optimization can be reduced, which is crucial for reliable tracking control when applied to real robotic systems. Using the proposed framework, jumping trajectories of legged robots are obtained in the simulation. Experimental validation of the algorithm is performed on a planar robot testbed, proving the effectiveness of the proposed method in generating dynamic motions of the legged robots.