Versatile Real-Time Motion Synthesis via Kino-Dynamic MPC with Hybrid-Systems DDP

Abstract

Specialized motions such as jumping are often achieved on quadruped robots by solving a trajectory optimization problem once and executing the trajectory using a tracking controller. This approach is in parallel with Model Predictive Control (MPC) strategies that commonly control regular gaits via online re-planning. In this work, we present a nonlinear MPC (NMPC) technique that unlocks on-the-fly re-planning of specialized motion skills and regular locomotion within a unified framework. The NMPC reasons about a hybrid kinodynamic model, and is solved using a variant of a constrained Differential Dynamic Programming (DDP) solver. The proposed NMPC enables the robot to perform a variety of agile skills like jumping, bounding, and trotting, and the rapid transition between these skills. We evaluated the proposed algorithm with three challenging motion sequences that combine multiple agile skills, on two quadruped platforms, Unitree A1, and MIT Mini Cheetah, showing its effectiveness and generality.

Hybrid Systems Differential Dynamic Programming for Whole-Body Motion Planning of Legged Robots

“…This result is not surprising, since both sides of the defect are considered in computing the search direction, thus facilitating faster convergence. is constructed based upon a hybrid kinodynamics (HKD) model [7], which reasons about then trunk dynamics and contact-dependent leg kinematics. In previous work [7], the HKD-MPC problem was solved using a SS-DDP variant that is tailored for hybrid systems [31].…”

“…is constructed based upon a hybrid kinodynamics (HKD) model [7], which reasons about then trunk dynamics and contact-dependent leg kinematics. In previous work [7], the HKD-MPC problem was solved using a SS-DDP variant that is tailored for hybrid systems [31]. In this work, we adapt the previous solver to use MS-DDP, and compare its performance against the previous SS-DDP implementation.…”

“…These properties make DDP exceptionally well suited for MPC with a long prediction horizon. In the past decade, DDP and its variants have been widely used for MPC of quadruped locomotion [3], [7], [8], humanoid balancing [9], [10], and loco-manipulation [11]. The downside of DDP, common with many other singleshooting algorithms, is that an initial guess for the state trajectory cannot be directly supplied, and it is sensitive to the initial guess of the control trajectory [12], [13].…”