cs.ROOct 3, 2026

DNPush: Distributed Nonparallel Pushing Force Control of Multi-Robot Systems for Object Transportation

Authors: Duy Anh Nguyen, Pham Duy Hung, Trung Dung Ngo

Organizations: More-Than-One Robotics Laboratory, Faculty of Sustainable Design Engineering, University of Prince Edward Island, Charlottetown, Canada · Faculty of Electronics and Telecommunications, VNU University of Engineering and Technology, Hanoi, Vietnam

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Abstract

This letter proposes DNPush, a Distributed Nonparallel Pushing force controller for cooperative object transport without inter-robot communication. Each robot uses local force measurements, a preassigned force weight, and a locally expressed desired transport direction, without requiring an object model, contact locations, a CoM estimate, or moment arm magnitudes online. DNPush regulates nonparallel force magnitudes from local force direction misalignments through a reciprocal-sine law. Under the stated contact conditions, Lyapunov analysis with LaSalle's invariance principle proves convergence to a unique rotational equilibrium, where perpendicular force contributions cancel and the net torque from normal forces is zero. Object velocity converges to the desired transport direction, and suitable contact regions exist for convex polygons. Simulations isolate the reciprocal-sine scaling mechanism, five-robot coordination, and active rotational damping. Hardware experiments with soft tactile differential-drive robots achieve a velocity direction error of 0.61 deg +/- 0.79 deg over five trials with a fixed transport direction and demonstrate object transport through waypoints with three robots.

Figures & tables

Fig. 1 : Core idea of DNPush. (a) For parallel pushing on a common object edge, reducing ∣Δi∣|\Delta_{i}| aligns the common pushing direction with the desired transport direction. (b) For nonparallel contacts, the same local alignment principle does not guarantee alignment of the resultant pushing force. (c) DNPush instead uses Δi\Delta_{i} to scale each pushing force, coordinating the force magnitudes while stabilizing object rotation without inter-robot communication.
Fig. 2 : Geometric and sensing notation for DNPush. (a) Contact geometry. (b) Local sensing and angular relations.
Fig. 3 : Guaranteed negative and positive moment contact regions near the vertex of a convex polygon closest to the CoM. The inward normals of the two adjacent edges have an angular separation smaller than π\pi .
Fig. 4 : Two-robot mechanism comparison under fixed nonparallel contacts. (a) Contact configuration. (b) Normal-force resultant component perpendicular to the desired transport direction. (c) Velocity direction error. (d) Object angular velocity.
Fig. 5 : Five-robot coordination with unequal moment sign groups. (a) Contact configuration with three robots in N\mathcal{N} and two in P\mathcal{P} . (b) Individual normal force magnitudes. (c) Perpendicular force contributions Fp,NF_{p,\mathcal{N}} and Fp,PF_{p,\mathcal{P}} and their resultant FpF_{p} .
Fig. 6 : Effect of active rotational damping with c0,r=c1,r=0c_{0,r}=c_{1,r}=0 . (a) Orientation error. (b) Object angular velocity.
Fig. 7 : Fixed-direction hardware repeatability over five trials.
Fig. 8 : Three-robot waypoint tracking with disturbances.
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