Robust Nonprehensile Object Transport with Quadruped Robots
Authors: Ainoor Teimoorzadeh, Riccardo Pretto, Mario Selvaggio, Gokhan Alcan, Sami Haddadin
Organizations: 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 · Mohamed Bin Zayed University of Artificial Intelligence, Masdar City, Abu Dhabi, UAE
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.
Figures & tables
Fig. 1: Picture of the problem addressed in this paper: A quadruped carries an unrestrained object on its back mounted flat platform from the initial point A to the final point B over an optimized sensitivity-aware trajectory planned for the reference frame {B} attached to the object.
Fig. 2: Schematic of the tray-based nonprehensile transportation model, in which a cylindrical object rests on a platform mounted on the back of a quadrupedal robot. The symbols are defined in Sec. II-B .
Fig. 3: Conceptual block scheme of the proposed control architecture. The sensitivity-based trajectory generator provides the desired object pose, twist, and its derivative to the coupled robot-object convex MPC. Using these references and the estimated robot and object states, the MPC computes the desired ground reaction forces and base accelerations. The whole-body controller maps these commands and the measured generalized state into the joint torque command applied to the quadruped.
Object CoM height
zb
0.35≤zb≤0.40m
Forward velocity
vb,x
∣vb,x∣≤1.0[m/s]
Lateral velocity
vb,y
∣vb,y∣≤0.05[m/s]
Vertical velocity
vb,z
∣vb,z∣≤0.2[m/s]
Control Parameters
Kp = diag (250,15)
Kd = diag (15,0.2)
TABLE I: Trajectory generation constraints and control parameters
Fig. 4: 3D visualization of the optimized robust object trajectories over a 5 s horizon for travel distances of 2 , 2.2 , and 2.4 m, shown in black, gray, and light gray, respectively. The object orientations are illustrated at intervals of 0.25 along the travel distance.
Fig. 5: Time evolution of a representative Λ for the optimized trajectories with travel distances of 2 , 2.2 , and 2.4 m. The thick solid curves represent the nominal solutions, the thin curves show the Monte Carlo realizations under ±10% perturbations of the object inertial parameters, and the dashed curves indicate the corresponding envelopes.
Fig. 6: Monte Carlo comparison of the optimized robust (top), fixed-orientation (middle), and straight-line (bottom) trajectories performed in the MuJoCo simulation environment. Each row shows representative snapshots and (a) robot CoM tracking error, (b) object RMS translation, and (c) object RMS orientation deviation. Blue, orange, and green denote 2 , 2.2 , and 2.4 m, respectively; error bars show the variation across realizations.
Fig. 7: Monte Carlo evaluation of the optimized trajectories under friction variations, with 30 realizations per coefficient.
Fig. 8: Time evolution of the object sliding for (a) the optimized trajectory and (b) straight-line baseline. The dashed curves represent the nominal case, while the dark and light curves correspond to +10% and −10% variations in the nominal object mass, respectively.