Multi-Rate Nonlinear Model Predictive Control for Wall-Supported Bipedal Locomotion of Quadrupedal Robots

This paper presents a novel layered planning and control framework based on multi-rate nonlinear model predictive control (MR-NMPC) that enables quadrupedal robots to perform hybrid bipedal locomotion with wall-assisted support in constrained environments. Real-time trajectory optimization for this locomotion presents significant challenges, as the controller must simultaneously plan for both the contact points and the continuous trajectories of the robot's center of mass (CoM) and orientation within the robot's nonlinear dynamics while accounting for unilateral contact constraints, underactuation, and the switching nature of the robot's dynamics. At the high level of the control framework, an MR-NMPC is proposed, which dynamically plans both the discrete-time trajectories of the contact points and the continuous-time trajectories of the CoM and orientation, using a single rigid body (SRB) dynamics model. By incorporating contact-point planning within the multi-rate optimal control framework, this approach enhances dynamic stability compared to heuristic foot placement strategies. At the low level of the control framework, a nonlinear whole-body controller (WBC) based on virtual constraints and a quadratic program enforces full-order dynamics and tracks the MR-NMPC references. The proposed approach is validated through extensive numerical simulations demonstrating the robust wall-assisted bipedal locomotion of a Unitree A1 quadrupedal robot on rough terrains and under external disturbances in a constrained environment. Comparative analysis shows that the proposed MR-NMPC achieves a 2.9 times higher success rate compared to conventional MPC with heuristic-based foot placement strategies in negotiating irregular terrain at high speeds.

Predictive Control with Indirect Adaptive Laws for Payload Transportation by Quadrupedal Robots

This paper formally develops a novel hierarchical planning and control framework for robust payload transportation by quadrupedal robots, integrating a model predictive control (MPC) algorithm with a gradient-descent-based adaptive updating law. At the framework's high level, an indirect adaptive law estimates the unknown parameters of the reduced-order (template) locomotion model under varying payloads. These estimated parameters feed into an MPC algorithm for real-time trajectory planning, incorporating a convex stability criterion within the MPC constraints to ensure the stability of the template model's estimation error. The optimal reduced-order trajectories generated by the high-level adaptive MPC (AMPC) are then passed to a low-level nonlinear whole-body controller (WBC) for tracking. Extensive numerical investigations validate the framework's capabilities, showcasing the robot's proficiency in transporting unmodeled, unknown static payloads up to 109% in experiments on flat terrains and 91% on rough experimental terrains. The robot also successfully manages dynamic payloads with 73% of its mass on rough terrains. Performance comparisons with a normal MPC and an L1 MPC indicate a significant improvement. Furthermore, comprehensive hardware experiments conducted in indoor and outdoor environments confirm the method's efficacy on rough terrains despite uncertainties such as payload variations, push disturbances, and obstacles.

A Nonlinear MPC Framework for Loco-Manipulation of Quadrupedal Robots with Non-Negligible Manipulator Dynamics

Model predictive control (MPC) combined with reduced-order template models has emerged as a powerful tool for trajectory optimization in dynamic legged locomotion. However, loco-manipulation tasks performed by legged robots introduce additional complexity, necessitating computationally efficient MPC algorithms capable of handling high-degree-of-freedom (DoF) models. This letter presents a computationally efficient nonlinear MPC (NMPC) framework tailored for loco-manipulation tasks of quadrupedal robots equipped with robotic manipulators whose dynamics are non-negligible relative to those of the quadruped. The proposed framework adopts a decomposition strategy that couples locomotion template models -- such as the single rigid body (SRB) model -- with a full-order dynamic model of the robotic manipulator for torque-level control. This decomposition enables efficient real-time solution of the NMPC problem in a receding horizon fashion at 60 Hz. The optimal state and input trajectories generated by the NMPC for locomotion are tracked by a low-level nonlinear whole-body controller (WBC) running at 500 Hz, while the optimal torque commands for the manipulator are directly applied. The layered control architecture is validated through extensive numerical simulations and hardware experiments on a 15-kg Unitree Go2 quadrupedal robot augmented with a 4.4-kg 4-DoF Kinova arm. Given that the Kinova arm dynamics are non-negligible relative to the Go2 base, the proposed NMPC framework demonstrates robust stability in performing diverse loco-manipulation tasks, effectively handling external disturbances, payload variations, and uneven terrain.

Safety-Critical and Distributed Nonlinear Predictive Controllers for Teams of Quadrupedal Robots

This paper presents a novel hierarchical, safety-critical control framework that integrates distributed nonlinear model predictive controllers (DNMPCs) with control barrier functions (CBFs) to enable cooperative locomotion of multi-agent quadrupedal robots in complex environments. While NMPC-based methods are widely adopted for enforcing safety constraints and navigating multi-robot systems (MRSs) through intricate environments, ensuring the safety of MRSs requires a formal definition grounded in the concept of invariant sets. CBFs, typically implemented via quadratic programs (QPs) at the planning layer, provide formal safety guarantees. However, their zero-control horizon limits their effectiveness for extended trajectory planning in inherently unstable, underactuated, and nonlinear legged robot models. Furthermore, the integration of CBFs into real-time NMPC for sophisticated MRSs, such as quadrupedal robot teams, remains underexplored. This paper develops computationally efficient, distributed NMPC algorithms that incorporate CBF-based collision safety guarantees within a consensus protocol, enabling longer planning horizons for safe cooperative locomotion under disturbances and rough terrain conditions. The optimal trajectories generated by the DNMPCs are tracked using full-order, nonlinear whole-body controllers at the low level. The proposed approach is validated through extensive numerical simulations with up to four Unitree A1 robots and hardware experiments involving two A1 robots subjected to external pushes, rough terrain, and uncertain obstacle information. Comparative analysis demonstrates that the proposed CBF-based DNMPCs achieve a 27.89% higher success rate than conventional NMPCs without CBF constraints.