This work introduces an optimization-based planning and control framework for real-time synthesis of whole-body motions for legged robots. At the core of the proposed framework is a cascaded-fidelity model predictive controller (Cafe-Mpc).Cafe-Mpcstrategically relaxes the planning problem along the prediction horizon (i.e., with descending model fidelity, increasingly coarse time steps, and relaxed constraints) for computational and performance gains. This problem is numerically solved with an efficient customized multiple-shooting iLQR solver that is tailored for hybrid systems. The action-value function fromCafe-Mpcis then used as the basis for a new value-function-based whole-body control (VWBC) technique that avoids additional tuning. In this respect, the proposed framework unifies whole-body MPC and more conventional whole-body quadratic programming, which have been treated as separate components in previous works. We study the effects of the cascaded relaxations inCafe-Mpcon the tracking performance and required computation time. We also show thatCafe-Mpc, if configured appropriately, advances the performance of whole-body MPC without necessarily increasing computational cost. Furthermore, we show the superior performance of VWBC over a conventional Riccati feedback controller in terms of constraint handling. The proposed framework enables accomplishing a gymnastic-style running barrel roll for the first time on quadruped hardware, whereCafe-Mpcruns at 50 Hz, and the solver spends on average 5.3 ms per iteration. Results are demonstrated in the accompanying video.

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 replanning 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 them. 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.

Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. It was originally designed as a single shooting method and thus is sensitive to the initial guess supplied. This work considers the extension of DDP to multiple shooting (MS), improving its robustness to initial guesses. A novel derivation is proposed that accounts for the defect between shooting segments during the DDP backward pass, while still maintaining quadratic convergence locally. The derivation enables unifying multiple previous MS algorithms, and opens the door to many smaller algorithmic improvements. A penalty method is introduced to strategically control the step size, further improving the convergence performance. An adaptive merit function and a more reliable acceptance condition are employed for globalization. The effects of these improvements are benchmarked for trajectory optimization with a quadrotor, an acrobot, and a manipulator. MS-DDP is also demonstrated for use in Model Predictive Control (MPC) for dynamic jumping with a quadruped robot, showing its benefits over a single shooting approach.

Seemingly in defiance of basic physics, cats consistently land on their feet after falling. In this paper, we design a controller that lands the Mini Cheetah quadruped robot on its feet as well. Specifically, we explore how trajectory optimization and machine learning can work together to enable highly dynamic bioinspired behaviors. We find that a reflex approach, in which a neural network learns entire state trajectories, outperforms a policy approach, in which a neural network learns a mapping from states to control inputs. We validate our proposed controller in both simulation and hardware experiments, and are able to land the robot on its feet from falls with initial pitch angles between −90 and 90 degrees.

Reinforcement Learning (RL) has witnessed great strides for quadruped locomotion, with continued progress in the reliable sim-to-real transfer of policies. However, it remains a challenge to reuse a policy on another robot, which could save time for retraining. In this work, we present a framework for zero-shot policy retargeting wherein diverse motor skills can be transferred between robots of different shapes and sizes. The new framework centers on a planning-and-control pipeline that systematically integrates RL and Model Predictive Control (MPC). The planning stage employs RL to generate a dynamically plausible trajectory as well as the contact schedule, avoiding the combinatorial complexity of contact sequence optimization. This information is then used to seed the MPC to stabilize and robustify the policy roll-out via a new Hybrid Kinodynamic (HKD) model that implicitly optimizes the foothold locations. Hardware results show an ability to transfer policies from both the A1 and Laikago robots to the MIT Mini Cheetah robot without requiring any policy re-tuning.