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Robust Nonprehensile Object Transport with Quadruped Robots

Ainoor Teimoorzadeh, Riccardo Pretto, Mario Selvaggio, Gokhan Alcan, Sami Haddadin

arXiv:2610.07245v1cs.RO

TL;DR

Quadruped transport of an unsecured object is challenging because gait disturbances and uncertain payload or contact properties affect motion. The paper combines sensitivity-aware trajectory planning with robot–object MPC and whole-body control. Simulations and hardware experiments report reduced sliding and lower robot CoM tracking errors against fixed-orientation and straight-line baselines.

  • Problem

    Unsecured payload transport on a quadruped couples object motion to gait disturbances, and joint planning and control for robustness to parameter uncertainty remains largely unexplored.

    Source: A. Related works · p. 2

  • Method

    The framework combines sensitivity-aware trajectory planning for an unsecured dorsal payload with MPC execution that accounts for payload dynamics and contact constraints.

    Source: A. Related works · p. 2

  • Results

    Optimized trajectories achieve lower robot CoM tracking errors and object translational deviation than fixed-orientation and straight-line baselines across the simulated travel distances, and hardware trials show lower final object displacement than straight-line trials.

    Source: §IV · pp. 7–8

  • Takeaways & Limitations

    The optimized motion combines bell-shaped vertical movement with backward and forward pitch rotations while exploiting the quadruped’s limited workspace.

    Source: §V · p. 8

Abstract

from arXiv · show

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.

I. INTRODUCTION

Nonprehensile transport keeps an ungrasped object on a tray-like surface, but quadruped locomotion adds disturbances and payload-induced shifts that complicate robust tracking. The paper combines sensitivity-aware trajectory optimization with coupled robot–object MPC and whole-body control for this setting.

I. INTRODUCTION

  • Dynamic nonprehensile transportation keeps a non-grasped object in contact with a tray-like end-effector throughout robot motion.Existing approaches include shared haptic control, QP-based methods, trajectory optimization, and MPC.Source: §I · p. 1
  • Quadruped gait impacts and chassis vibrations create unpredictable friction variations, while the payload shifts the robot’s center of mass and complicates precise tracking.These effects motivate robust control for an unsecured object carried on a legged platform.Source: §I · p. 1
  • The framework uses closed-loop sensitivity-based trajectory optimization to generate object-centric motions, tracked by coupled robot–object MPC and a whole-body controller.The contributions also include simulation and hardware validation showing reduced object sliding against baseline trajectories.Source: §I · p. 2

A. Related works

Prior nonprehensile transport methods often assume accurate object and contact models, while work on quadrupeds has not jointly addressed an unsecured payload and sensitivity to parameter uncertainty. This paper combines sensitivity-aware planning with MPC execution on the robot’s dorsal carrying surface.

A. Related works

  • Many trajectory-planning methods assume accurate object and contact properties, and an object-aware MPC approach still relies on a known object model.Robust sticking constraints address uncertainty at the planning level, while sensitivity-aware approaches have been explored in nonprehensile manipulation but not jointly with legged transport.Source: A. Related works · p. 2
  • An arm-based quadruped architecture adds mass and mechanical complexity, whereas LocoTouch uses tactile-reactive locomotion rather than model-based robustness to uncertain object and contact parameters.These approaches address different trade-offs and goals for quadruped object transport.Source: A. Related works · p. 2
  • Quadruped carrying couples payload motion to locomotion, intermittent ground contacts, body stabilization, and payload dynamics, with gait oscillations and foot impacts able to excite sliding or tipping.Errors in mass distribution, inertia, or contact properties alter predicted payload motion and its interaction with the robot.Source: A. Related works · p. 2
  • The paper combines sensitivity-aware trajectory planning and MPC execution for an unsecured object on the quadruped’s dorsal surface, shaping the closed-loop response to parameter uncertainty and gait disturbances.The task considers a cylindrical object on a flat back-mounted surface, transported between prescribed points with minimal sensitivity to dynamic parameters, including friction.Source: A. Related works · p. 2

II. PRELIMINARIES & OBJECT MODELING

This section supplies background on closed-loop sensitivity and the object-and-friction model used to explain the methodology.

II. PRELIMINARIES & OBJECT MODELING

  • The section introduces closed-loop sensitivity as background for the methodology.It also provides background on the adopted object and friction model.Source: §II · p. 3

A. Closed-Loop Sensitivity

Closed-loop state and input sensitivities quantify how parameter variations affect system behavior. The paper uses these sensitivities to shape trajectory references for reduced variation under uncertain parameters.

A. Closed-Loop Sensitivity

  • The system state, input, and parameters are denoted x, u, and p; for this transport task, p includes object inertial parameters and the friction coefficient.The controller tracks a desired reference trajectory using nominal parameters.Source: A. Closed-Loop Sensitivity · p. 3
  • The controller uses a nominal parameter vector and has no knowledge of the true parameters.The controller dynamics and control input are expressed in terms of its state, the system state, the desired reference, and nominal parameters.Source: A. Closed-Loop Sensitivity · p. 3
  • Closed-loop state and input sensitivities describe variations in system state and control caused by parameter variation.The sensitivities are obtained by integration and quantify robustness to parameter changes.Source: A. Closed-Loop Sensitivity · p. 3
  • First-order approximations of state and input changes yield uncertainty ellipsoids, and parameter uncertainty is represented within specified bounds by an ellipsoid.These sensitivity-based quantities can be used to optimize reference trajectories for minimal variation or estimate uncertainty tubes and enforce physical bounds.Source: A. Closed-Loop Sensitivity · p. 3

B. Object Modeling

The object is modeled as a rigid body with frictional point contacts on the carrying platform. Its body-frame dynamics and contact forces define the wrench transmitted to it.

B. Object Modeling

  • The object is modeled as a rigid body whose body-frame dynamics use a mass matrix built from its mass and inertia.The model also includes Coriolis, centrifugal, and gravitational effects.Source: B. Object Modeling · p. 3
  • Four frictional point contacts around the circular object's perimeter transmit forces, but no moments, to the body.The contact model is described as a conservative approximation of the true contact evolution.Source: B. Object Modeling · pp. 3–4
  • The contact forces are combined into a body wrench through the contact-point mapping.The admissible body wrench is expressed using the resulting contact-force representation.Source: B. Object Modeling · p. 4
  • Each contact's friction cone is conservatively approximated by an inscribed polyhedral cone, with four generators giving a pyramidal approximation.The model enforces non-sliding conditions by requiring the contact coefficients to remain nonnegative.Source: B. Object Modeling · p. 4

A. Robust Trajectory Generation

The trajectory generator selects object motions to reduce closed-loop sensitivity to parameter variations while respecting contact feasibility. It parameterizes the desired translation and rotation with polynomials.

A. Robust Trajectory Generation

  • The generator parameterizes desired object translation and rotation with eighth-degree polynomials, deriving velocities and accelerations from their derivatives.The polynomial coefficients form the optimization variable.Source: A. Robust Trajectory Generation · p. 4
  • The trajectory optimization selects coefficients to minimize the dynamical system's sensitivity to parameter variations.The uncertain parameters include object inertial properties and friction between the object and the platform.Source: A. Robust Trajectory Generation · p. 4
  • The trajectory generator supplies desired object pose, twist, and derivatives to the coupled robot-object MPC.The closed-loop dynamics combine the object model with its trajectory-tracking control law.Source: Figure 3 · p. 4, A. Robust Trajectory Generation · pp. 4–5
  • Sensitivity tubes constrain contact forces to remain within friction cones under considered parameter variations, preserving contact feasibility.The input-tube lower boundary is constrained to remain inside the polyhedral friction cone.Source: A. Robust Trajectory Generation · pp. 4–5

B. Coupled Robot-Object Convex MPC Modeling

The convex MPC jointly predicts robot and object motion, optimizing ground-reaction forces and object-platform contact wrench. Softened motion-coupling conditions link their accelerations.

B. Coupled Robot-Object Convex MPC Modeling

  • The coupled MPC jointly optimizes ground-reaction forces and object-platform contact wrench using a robot-object centroidal model.The robot model uses single-rigid-body dynamics, and the contact wrench's equal-and-opposite reaction enters the robot dynamics.Source: B. Coupled Robot-Object Convex MPC… · p. 5
  • Softened acceleration-level conditions couple object and platform motion, with a slack variable allowing deviations from perfect motion coupling.The object acceleration includes robot acceleration and rotational terms evaluated along the nominal trajectory.Source: B. Coupled Robot-Object Convex MPC… · p. 5
  • At each control update, the MPC solves a finite-horizon QP with feasible ground-reaction forces, including friction constraints and zero swing-foot forces.Configuration-dependent model terms are linearized along the nominal trajectory and discretized at the MPC sampling time.Source: B. Coupled Robot-Object Convex MPC… · p. 5

C. Whole-Body Inverse-Dynamics Control

The whole-body inverse-dynamics QP tracks the MPC’s centroidal commands using full floating-base dynamics. It enforces stance-foot, ground-reaction-force, and actuator constraints, and returns desired robot acceleration and ground-reaction forces.

C. Whole-Body Inverse-Dynamics Control

IV. SIMULATION AND HARDWARE VALIDATION

Simulations and hardware trials assess the optimized trajectories under object-parameter and friction variations. The optimized motion improves robot CoM tracking and object transport relative to the stated baselines, while hardware tests use the robot’s default controller.

Simulation and hardware validation

  • The optimized trajectories use a bell-shaped vertical profile with backward and forward pitch rotations rather than following a straight line.The paper interprets vertical motion as increasing normal contact force during upward acceleration and pitch as potentially compensating for limited vertical workspace.Source: Figure 4 · p. 6, §IV · p. 6
  • Across 30 Monte Carlo realizations with object parameters perturbed by ±10%, the contact-coefficient evolution remains within the predicted sensitivity tubes.The trajectories were evaluated in MuJoCo, calibrated using motion-capture data.Source: §IV · p. 6, Figure 5 · p. 7
  • Increasing friction generally reduces object sliding, especially on longer trajectories, while robot CoM tracking error remains nearly unaffected by friction variations.The evaluation covered five friction coefficients, three travel distances, and 30 mass realizations per combination, totaling 450 simulations.Source: §IV · p. 7
  • Hardware validation used a cylindrical object on a back-mounted platform, testing three travel distances, two trajectory types, and three mass values in 180 trials.The object was free to slide, with nominal mass 0.07 kg and nominal simulated friction coefficient µ = 0.52.Source: §IV · pp. 6–7
  • The optimized trajectory achieves the lowest robot CoM tracking error and object translational deviation across 2.0, 2.2, and 2.4 m, compared with fixed-orientation and straight-line baselines.Object orientation deviation remains relatively high for the optimized trajectory as its motion becomes more dynamic.Source: Figure 6 · p. 7, §IV · p. 7
  • In hardware trials, optimized trajectories recover from increased midpoint sliding and yield lower final object displacement than the straight-line baseline.The robot’s default controller was used for every trial, isolating the effect of trajectory design rather than testing the proposed whole-body controller.Source: Figure 8 · p. 8, §IV · p. 8

V. CONCLUSIONS

The paper presents a quadruped framework for robust nonprehensile object transport, combining sensitivity-aware trajectory optimization with robot-object control. Simulations and hardware experiments report reduced sliding and lower CoM tracking errors against the stated trajectory baselines; future work targets full hardware control and broader settings.

V. Conclusions

  • The framework combines closed-loop sensitivity-based trajectory optimization with coupled robot-object MPC and whole-body control for an unsecured payload on a quadruped’s back.The generated motion combines bell-shaped vertical movement with backward and forward pitch rotations.Source: §V · p. 8
  • MuJoCo evaluations report lower robot CoM tracking errors and reduced object sliding than fixed-orientation and straight-line baselines, while hardware trials show benefits under payload mass variations.The hardware experiments used the robot’s native controller.Source: §V · p. 8
  • Future work will implement the complete control framework on hardware and extend evaluation to broader object geometries and larger parameter uncertainties.Source: §V · p. 8
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