Kaveh Akbari Hamed

Model predictive control (MPC) with reduced-order template models has proven effective for dynamic legged locomotion, but loco-manipulation introduces additional complexity requiring efficient algorithms for high-degree-of-freedom (DoF) systems. 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 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. The optimal state and input trajectories generated by the NMPC for locomotion are tracked by a low-level nonlinear whole-body controller, 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 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.

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 used to enforce safety constraints and navigate multi-robot systems (MRSs) through complex environments, trajectory optimization frameworks based on invariant sets offer formal safety guarantees for MRSs. 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 results demonstrate that the proposed CBF-integrated DNMPC achieves a higher success rate than baseline NMPCs employing CBFs at the high or low-level layers.

This paper aims to develop a distributed layered control framework for the navigation, planning, and control of multi-agent quadrupedal robots subject to environments with uncertain obstacles and various disturbances. At the highest layer of the proposed layered control, a reference path for all agents is calculated, considering artificial potential fields (APF) under a priori known obstacles. Second, in the middle layer, we employ a distributed nonlinear model predictive control (NMPC) scheme with a one-step delay communication protocol (OSDCP) subject to reduced-order and linear inverted pendulum (LIP) models of agents to ensure the feasibility of the gaits and collision avoidance, addressing the degree of uncertainty in real-time. Finally, low-level nonlinear whole-body controllers (WBCs) impose the full-order locomotion models of agents to track the optimal and reduced-order trajectories. The proposed controller is validated for effectiveness and robustness on up to four A1 quadrupedal robots in simulations and two robots in the experiments.1 Simulations and experimental validations demonstrate that the proposed approach can effectively address the real-time planning and control problem. In particular, multiple A1 robots are shown to navigate various environments, maintaining collision-free distances while being subject to unknown external disturbances such as pushes and rough terrain.

This letter 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 $\mathcal {L}_{1}$ 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.

This paper formally develops robust optimal predictive control solutions that can accommodate disturbances and stabilize periodic legged locomotion. To this end, we build upon existing optimization-based control paradigms, particularly quadratic programming (QP)-based model predictive controllers (MPCs). We present conditions under which the closed-loop reduced-order systems (i.e., template models) with MPC have the continuous differentiability property on an open neighborhood of gaits. We then linearize the resulting discrete-time, closed-loop nonlinear template system around the gait to obtain a linear time-varying (LTV) system. This periodic LTV system is further transformed into a linear system with a constant state-transition matrix using discrete-time Floquet transform. The system is then analyzed to accommodate parametric uncertainties and to synthesize robust optimal H₂ and H_∞ feedback controllers via linear matrix inequalities (LMIs). The paper then extends the theoretical results to the single rigid body (SRB) template dynamics and numerically verifies them. The proposed robust optimal predictive controllers are used in a layered control structure, where the optimal reduced-order trajectories are provided to a full-order nonlinear whole-body controller (WBC) for tracking at the low level. The developed layered controllers are numerically and experimentally validated for the robust locomotion of the A1 quadrupedal robot subject to various disturbances and uneven terrains. Our numerical results suggest that the H₂ - and H_∞ -optimal MPC controllers significantly improve the robust stability of the gaits compared to the normal MPC.

This work aims to provide a computationally effective and distributed trajectory planner at the intersection of physics-based and data-driven techniques for the collaborative locomotion of holonomically constrained quadrupedal robots that can account for and attenuate interaction forces between subsystems. More specifically, this work lays the foundation for using an interconnected single rigid body model in a predictive control framework such that interaction forces can be utilized at the planning layer, wherein these forces are parameterized via a behavioral systems approach. Furthermore, the proposed trajectory planner is distributed such that each agent can locally plan for its own trajectory subject to coupling dynamics, resulting in a much more computationally efficient method for real-time planning. The optimal trajectory obtained by the planner is then provided to a full-order nonlinear whole-body controller for tracking at the low level. The efficacy and robustness of the proposed approach are verified both in simulation and on hardware subject to various disturbances, payloads, and uneven terrains.

This article presents a layered control approach for real-time trajectory planning and control of robust cooperative locomotion by two holonomically constrained quadrupedal robots. A novel interconnected network of reduced-order models, based on the single rigid body (SRB) dynamics, is developed for trajectory planning purposes. At the higher level of the control architecture, two different model predictive control (MPC) algorithms are proposed to address the optimal control problem of the interconnected SRB dynamics: centralized and distributed MPCs. The distributed MPC assumes two local quadratic programs that share their optimal solutions according to a one-step communication delay and an agreement protocol. At the lower level of the control scheme, distributed nonlinear controllers are developed to impose the full-order dynamics to track the prescribed reduced-order trajectories generated by MPCs. The effectiveness of the control approach is verified with extensive numerical simulations and experiments for the robust and cooperative locomotion of two holonomically constrained A1 robots with different payloads on variable terrains and in the presence of disturbances. It is shown that the distributed MPC has a performance similar to that of the centralized MPC, while the computation time is reduced significantly.

The aim of this work is to define a planner that enables robust legged locomotion for complex multi-agent systems consisting of several holonomically constrained quadrupeds. To this end, we employ a methodology based on behavioral systems theory to model the sophisticated and high-dimensional structure induced by the holonomic constraints. The resulting model is then used in tandem with distributed control techniques such that the computational burden is shared across agents while the coupling between agents is preserved. Finally, this distributed model is framed in the context of a predictive controller, resulting in a robustly stable method for trajectory planning. This methodology is tested in simulation with up to five agents and is further experimentally validated on three A1 quadrupedal robots subject to various uncertainties, including payloads, rough terrain, and push disturbances.

This paper presents a layered control approach for real-time trajectory planning and control of robust cooperative locomotion by two holonomically constrained quadrupedal robots. A novel interconnected network of reduced-order models, based on the single rigid body (SRB) dynamics, is developed for trajectory planning purposes. At the higher level of the control architecture, two different model predictive control (MPC) algorithms are proposed to address the optimal control problem of the interconnected SRB dynamics: centralized and distributed MPCs. The distributed MPC assumes two local quadratic programs that share their optimal solutions according to a one-step communication delay and an agreement protocol. At the lower level of the control scheme, distributed nonlinear controllers are developed to impose the full-order dynamics to track the prescribed reduced-order trajectories generated by MPCs. The effectiveness of the control approach is verified with extensive numerical simulations and experiments for the robust and cooperative locomotion of two holonomically constrained A1 robots with different payloads on variable terrains and in the presence of disturbances. It is shown that the distributed MPC has a performance similar to that of the centralized MPC, while the computation time is reduced significantly.