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.
Figures & tables
Fig. 1: Snapshot of the locomotion of the A1 robot with a payload of 11.34 (kg) ( 91% uncertainty) on wooden blocks using the proposed AMPC.
Fig. 2: Overview of the proposed layered control approach with the AMPC algorithm and the adaptive gradient law at the high level ( 160 Hz) and the nonlinear WBC at the low level ( 1 kHz) for robust locomotion with unknown payloads.
Fig. 3: Snapshots of experiments for (a) flat terrain locomotion with a 13.6 (kg) payload ( 109% uncertainty); (b) and (c) rough terrain locomotion with wooden blocks and 11.34 (kg) ( 91% uncertainty) and 8.2 (kg) payloads; (d) dynamic payload addition; (e) pushing the robot with a 6.48 (kg) payload; (f), pushing a 3.7 (kg) object while carrying a 4.5 (kg) payload; (g) and (h) locomotion on grass and gravel with a 6.48 (kg) payload; (i) and (j) backward and lateral trot on rough terrain with 9 (kg) and 6.8 (kg) payloads and a COM offset. In all of these experiments, the desired forward velocities are 0.5 (m/s), except for (b) and (d), which are 0.4 (m/s) and 0.6 (m/s), respectively. For the backward and lateral trot, the desired velocity is 0.4 (m/s) and 0.15 (m/s).
Fig. 4: Plot of the prescribed reduced-order trajectory and vertical GRF for the front right leg by the AMPC planner at the forward speed of 0.4 (m/s) in (a) and (b). (c) Evolution of the estimated mass parameter. Despite the challenges posed by uneven terrain and an unknown payload of 11.34 (kg), the robot demonstrates robust locomotion, as depicted in Fig. 3 (b).
Fig. 5: Plot of the prescribed reduced-order trajectory and vertical GRF for the front right leg by the AMPC planner at the forward speed of 0.6 (m/s) in (a) and (b). (c) Evolution of the estimated mass parameter. The robot is subject to carrying a payload of 6.48 (kg) and dynamic additions, as shown in Fig. 3 (d). The true mass varies in response to these dynamic payload additions.
Fig. 6: The success rates of various predictive control algorithms, including the AMPC, normal MPC, and L1 MPC with a 6.5 (kg) payload on 1500 randomly generated rough terrains versus the distance.
In this paper, we present a robust nonprehensile object transportation framework for quadruped robots. An uncertainty-aware trajectory optimization method generates object motions with minimal closed-loop sensitivity to uncertain parameters. The resulting reference trajectory is tracked using a coupled convex model predictive controller that jointly predicts the CoM dynamics of the quadruped and the payload followed by a whole-body QP that enforces ground reaction constraints. The approach is evaluated through extensive simulations and real-world experiments under variations in the object's inertial parameters. Its performance is compared with fixed-orientation and straight-line trajectories as baseline. The results show that the optimized object motion reduces the sliding by approximately 50% compared with the fixed-orientation baseline and 30% compared with the straight-line baseline, while also achieving lower robot CoM tracking errors.
Ainoor Teimoorzadeh, Riccardo Pretto, Mario Selvaggio +2
Munich Institute of Robotics & Machine Intelligence, Technical University of Munich (TUM), Munich, Germany · Tampere University, Finland · PRISMA Lab, Department of Electrical Engineering and Information Technology, University of Naples Federico II, Via Claudio 21, 80125, Naples, Italy +1
Load transportation with quadruped robots is strongly affected by the dynamics of the physical interface between the robot and the load. Passive spring-based arms provide a lightweight and mechanically compliant alternative to active manipulators, but their dynamics can store and release energy during locomotion, producing oscillatory interaction forces that reduce robot stability. This paper develops a passive-arm-aware ZMP model for a quadruped carrying a payload through a passive arm. The reduced analytical model relates passive-interface stiffness, damping, and payload mass to the ZMP response under both external payload forcing and locomotion-induced base excitation, showing that lightly damped passive modes can overlap with gait harmonics. We then propose an arm-aware MPC (ARMPC), a passive-arm Model Predictive Control approach based on extended Single Rigid Body Dynamics that combines reduced floating-base dynamics with passive-arm joint states, internal torsional springs and dampers, and base-arm inertial coupling. Simulation ablations show that ARMPC consistently reduces ZMP-margin violations and prevents failures across all tested conditions, while Nominal MPC, which neither models nor compensates the passive arm, and Baseline MPC, which compensates it through an estimated wrench, exhibit higher violation percentages and failures under disturbances. Hardware pull-release experiments with a 2 kg payload show that the proposed ARMPC completes all longitudinal and diagonal disturbance trials without failure, whereas Baseline MPC fails in 7/15 and 8/15 trials, respectively. The same model also enables passive-arm end-effector tracking while maintaining a positive ZMP margin.
Giovanni B. Dessy, Lorenzo Amatucci, Claudio Semini +1
Dynamic Legged Systems Lab, Istituto Italiano di Tecnologia (IIT).
Humanoid robots performing lifting and material-handling tasks must maintain balance despite unknown and varying payloads. However, payload uncertainty significantly affects whole-body dynamics and may destabilize conventional controllers. We propose an adaptive whole-body control architecture that integrates three components: (i) a centroidal model predictive controller (MPC) that generates dynamically feasible reference motions, (ii) an adaptive fuzzy balance controller that compensates for payload-induced model mismatch by generating corrective torques distributed across the supporting-leg joints, and (iii) a waypoint-based optimal posture planner built on a triple-integrator model that produces smooth sit-to-stand and stand-to-sit trajectories satisfying center-of-mass (CoM) stability constraints, joint limits, and whole-body feasibility requirements. Together, these components enable stable lowering, grasping, lifting, carrying, and placing behaviors under significant payload uncertainty. Extensive simulation and hardware experiments demonstrate that the proposed framework improves balance robustness and reduces tracking degradation during posture transitions and lifting tasks compared to non-adaptive baselines.
Manh Cuong Nguyen, Duc Cuong Vu, Viet Anh Vu +5
VinRobotics, Vingroup, Hanoi 10000, Vietnam · Center for AI Research (CAIR), VinUniversity, Hanoi 10000, Vietnam