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Communication-Free Obstacle Localization from Aggregate Wrench Measurements in Leader--Follower Cooperative Transport

Amin Kashiri, Aditya Mohan, Yasin Yazıcıoğlu

arXiv:2610.08324v1cs.ROcs.MAcs.SYeess.SY

TL;DR

A leader cannot tell which follower reacted to an obstacle from their aggregate wrench alone. The paper designs a follower reaction law and probing procedure that expose obstacle information in the twist-to-wrench map. Under stated fixed-pose conditions, adjacent-cell observations support exact recovery, and simulations report recovery across designed and random scenes.

  • Problem

    With several followers, their reactions are summed into a three-number aggregate wrench, so a measurement does not reveal which follower responded or to what.

    Source: §I · p. 1

  • Method

    A follower law makes the aggregate wrench piecewise linear in payload twist, and the leader probes the payload to collect measurements across adjacent cells.

    Source: §I · p. 1, B. Piecewise-linear map from twist to… · p. 3, A. Probes, samples and local matrices · p. 4

  • Results

    All 17 designed-scene pairs were found at every gain from 1000 N s/m; random-scene recovery reached 140 of 147 pairs at 108 N s/m.

    Source: B. Recovery · p. 6

  • Takeaways & Limitations

    At a fixed pose, under the theorem’s conditions, adjacent-cell observations recover the obstacle center and the follower that detected it exactly.

    Source: D. Exact recovery guarantee · pp. 3–4

    Evaluation is in simulation; formal guarantees for collecting observations needed for exact recovery and real-robot testing remain future work.

    Source: §I · p. 1, §VI · p. 6

Abstract

from arXiv · show

We consider obstacle localization for a team of robots cooperatively transporting a rigid payload without explicit inter-robot communication. A leader robot directs the payload's motion, while follower robots assist and react to locally detected obstacles. The leader measures the followers' aggregate wrench, i.e., the combined force and torque they exert on the payload, but cannot directly distinguish their individual reactions. We design a follower control law that allows the leader to recover obstacle locations from these measurements. Each follower resists motion toward nearby obstacles, resulting in a piecewise-linear relationship between the payload's translational and angular velocity and the aggregate wrench. Changes between adjacent linear regions reveal an obstacle's bearing and distance and identify the responding follower. We give sufficient conditions for exact recovery at a fixed payload configuration and develop an adaptive probing procedure in which the leader applies translational and rotational inputs to the payload to obtain the required measurements. We demonstrate the performance of the proposed method in simulations.

I. INTRODUCTION

In communication-free cooperative transport, the leader must infer obstacle reactions that are hidden within the followers’ aggregate wrench. The paper proposes active probing and a follower law to separate those reactions, within a team model where only the leader knows the destination.

I. INTRODUCTION

  • In leader–follower transport without communication, the payload is the only coordination channel: a destination-informed leader steers it while each follower reinforces motion measured at its grip; obstacle information is absent or supplied to the planning robot,.In a two-robot team, a leader recovers obstacles from the input of the single follower.Source: §I · p. 1
  • The leader measures only a three-number aggregate wrench, so a single measurement cannot identify which follower reacted or to what.The paper targets this attribution problem when multiple followers detect obstacles.Source: §I · p. 1
  • A follower law makes the twist-to-wrench map piecewise linear, so boundaries between regions encode obstacle bearing, distance, and responding follower.The leader actively probes the payload to separate the reactions; fixed-pose recovery conditions and an adaptive probing procedure are developed.Source: §I · p. 1

A. Setup

  • In the modeled team, the leader alone knows the destination; followers lack world positions, destination knowledge, and observations of other robots’ states or inputs.The robots do not explicitly communicate.Source: A. Setup · p. 1
  • Obstacles are stationary disks of known radius, and a follower detects an obstacle center when it lies within the activation distance of its grip.An obstacle detected by multiple followers forms a separate obstacle–follower pair for each follower.Source: A. Setup · p. 2

B. System model

The system model relates each robot’s grip motion and applied forces to payload motion and wrench. Followers compensate for modeled viscous friction, while the leader directs the payload and can compute their aggregate wrench.

B. System model

  • A grip’s velocity combines the payload’s center-of-mass velocity with the velocity induced by payload rotation.The rigid-body relation connects each robot’s local grip measurement to motion of the whole payload.Source: B. System model · p. 2
  • A robot’s payload wrench includes its grip force, the moment from the grip offset, and any torque applied directly through the grip.The grip geometry maps local forces into payload force and moment.Source: B. System model · p. 2
  • Each follower compensates for a share of modeled viscous friction, while the leader selects desired translational and angular velocities to direct the team.The controller is also used to generate obstacle-localization probes.Source: B. System model · p. 2
  • The leader computes the followers’ aggregate wrench from measured accelerations and its own wrench; the carrying-only matrix contains no obstacle information.Obstacle localization uses the obstacle-dependent reaction added to that baseline wrench.Source: B. System model · p. 2

III. OBSTACLE RECOVERY

The recovery analysis studies obstacle-dependent wrench measurements while the payload configuration is fixed. It establishes recovery conditions and motivates finite-duration probing to collect the needed observations.

III. OBSTACLE RECOVERY

  • The section designs a follower reaction law and establishes conditions for recovering obstacle locations and responding followers from aggregate wrench measurements.The analysis treats a fixed payload configuration, holding grip positions, obstacle distances, and bearings fixed as twist varies.Source: §III · p. 2
  • Exact-recovery analysis assumes grip positions, obstacle distances, and bearings remain fixed while payload twist varies.This is the scope of the analysis described for this section.Source: §III · p. 2
  • The leader collects the required measurements using finite-duration probing motions, described in the following section.The probing procedure is distinct from the fixed-configuration recovery analysis.Source: §III · p. 2

A. Follower reaction law

Followers resist only motion toward nearby obstacles, making the aggregate wrench a piecewise-linear function of payload twist. Switching boundaries partition twist space into cells and carry information about the reacting obstacle–follower pair.

A. Follower reaction law

  • Each active follower–obstacle pair reacts only when the follower moves toward the obstacle; its reaction points away, grows with approach speed, and vanishes at rest.The reaction magnitude is weighted by a specified, strictly decreasing function of obstacle distance.Source: A. Follower reaction law · p. 2

B. Piecewise-linear map from twist to wrench

  • Fig. 1 depicts switching planes as great circles on a sphere, with a shaded cell and a translation circle marked by crossings and sample centers.Each sample center is surrounded by three probes, whose spread is exaggerated in the figure.Source: Figure 1 · p. 3
  • A pair’s switching plane divides twist space into cells, within each of which the set of resisting pairs is fixed.Each cell is a cone from the origin.Source: B. Piecewise-linear map from twist to… · p. 3
  • Within a cell, each resisting pair contributes a linear wrench term and nonresisting pairs contribute zero, making the aggregate wrench linear there.The pair’s wrench direction also determines when it resists.Source: B. Piecewise-linear map from twist to… · p. 3

C. Recovery from observations

The leader estimates local linear maps from observations within cells, then uses the change between adjacent maps to recover an obstacle’s bearing, distance, and responding follower.

C. Recovery from observations

D. Exact recovery guarantee

At a fixed pose, the theorem guarantees exact recovery when active pairs have distinct bearings, followers have distinct moment arms in each bearing direction, and each adjacent cell is sufficiently observed.

D. Exact recovery guarantee

  • Exact recovery assumes distinct signed moment arms for followers in each active pair’s bearing direction and no parallel or opposite bearings between distinct pairs.Source: D. Exact recovery guarantee · p. 3
  • Under these assumptions, three linearly independent twist observations in each of two adjacent cells suffice to recover the separating pair’s follower and obstacle center.Source: D. Exact recovery guarantee · pp. 3–4
  • Distinct bearings ensure only the target pair switches between the cells, while distinct moment arms make its follower uniquely identifiable.Source: D. Exact recovery guarantee · p. 4

IV. THE PROBING PROCEDURE

The probing procedure searches for observations needed by the recovery theorem, using repeated out-and-back motions to estimate local maps and refine intervals where switching may occur.

IV. THE PROBING PROCEDURE

  • The procedure searches for the observations required by Theorem 1 and uses them to estimate obstacle locations.Source: §IV · p. 4

A. Probes, samples and local matrices

B. The procedure

  • Initial samples are evenly spaced around the pure-translation circle, whose crossings mark where a follower-obstacle pair starts or stops resisting.Source: B. The procedure · p. 4
  • For neighboring samples, the procedure treats near-zero jumps as no switch, reconstructs nearly rank-one jumps, and subdivides other intervals until unresolved or narrow enough.Source: B. The procedure · pp. 4–5
  • Reconstructed candidates are rejected when checks fail and merged when they identify the same follower with nearby obstacle centers.Source: B. The procedure · p. 5

A. Setup

The simulations evaluate the procedure on five designed scenes and thirty random scenes, using a distance-based criterion to count found pairs and false positives.

A. Setup

  • The first evaluation set contains five designed scenes at the reference pose, shown with their numbers of active pairs.Source: A. Setup · p. 5, Figure 3 · p. 5
  • The second set contains thirty fixed-seed random scenes, each with 3 to 6 followers and randomized balanced grip positions around an ellipse.Source: A. Setup · p. 5
  • The random scenes contain 147 active follower-obstacle pairs in total, with obstacles placed 0.55–0.9 m away and outside the payload and robots.Source: A. Setup · p. 5
  • A pair counts as found when an estimate names its follower and lies within 5 cm of its obstacle; unmatched estimates are false positives.Source: A. Setup · p. 5

B. Recovery

Recovery improves along the probing parameter schedule: random-scene recovery reaches 140 of 147 pairs, while all 17 designed-scene pairs are found at gains from 1000 N s/m. Exact recovery is conditional on observations across adjacent cells, and guaranteed collection of those observations remains future work.

B. Recovery

  • At 100 N s/m, the procedure finds 15 of 17 designed-scene pairs and 54 of 147 random-scene pairs, with three false positives in random scenes.Real probes are recorded near, rather than exactly at, the reference pose, and their twists differ slightly from the commanded ones.Source: B. Recovery · p. 5
  • 140 of 147 random-scene pairs are found at 108 N s/m, while all 17 designed-scene pairs are found at every gain from 1000 N s/m.The random-scene results include one false positive at 105 N s/m and none from 106 N s/m; the schedule uses shorter probes, faster re-centering, smaller spread, and smaller tolerances.Source: Table II · p. 6, Table III · p. 6, B. Recovery · p. 6

VI. CONCLUSION

  • A single follower–obstacle pair's start or stop produces a rank-one change in the wrench map, enabling closed-form recovery when adjacent cells meet the stated observation conditions.The leader's probing procedure searches for these observations by comparing neighboring samples and splitting intervals where several pairs switch.Source: §VI · p. 6
  • The probing procedure does not yet formally guarantee collection of observations sufficient for exact recovery.Formal guarantees for collecting those observations and tests on real robots are identified as future work.Source: §VI · p. 6

APPENDIX: IMPLEMENTATION DETAILS

Each sample uses three nearby twist probes around a translation-circle direction. The leader re-centers, performs an out-and-back motion for each probe, and records the return near a consistent payload position.

APPENDIX: IMPLEMENTATION DETAILS

  • Each sample uses three probes whose twists combine a center direction with spread along the tangent and rotational directions.The three probes use phases ψj and are normalized to speed α.Source: APPENDIX: IMPLEMENTATION DETAILS · p. 6
  • Before each probe, the leader re-centers the payload toward the reference pose using gain gr for a fixed duration.The reference pose is xref = [p⊤c,ref, θref]⊤.Source: APPENDIX: IMPLEMENTATION DETAILS · p. 6
  • For each probe, the leader commands −νp,j and then νp,j, recording twist and aggregate wrench during the return.It records at the first instant the payload is moving back toward the reference center-of-mass position.Source: APPENDIX: IMPLEMENTATION DETAILS · pp. 6–7
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