Source-linked AI summary
Contact as a Decision Variable: Capability-Tradeoff Contact Selection for Legged Loco-Manipulation
Al Jaber Mahmud, Shuai Li, Xuan Wang
TL;DR
Legged loco-manipulation requires support that sustains task loads without unduly restricting required motion, and evaluating every candidate support can require repeated whole-body optimizations. CTCS screens feasibility and predicts candidate capabilities using local sensitivity analysis within surface-specific groups. In simulations and hardware experiments, it closely matched exhaustive evaluation's mean objective while requiring less computation.
Problem
Choosing support is a task-dependent trade-off because a contact can provide physical support while restricting the motion needed for manipulation or locomotion, and evaluating many candidates requires repeated whole-body optimization.
Source: §I · p. 1, §IV · p. 4Method
CTCS screens contact and task feasibility, groups similar candidates within each surface, predicts capabilities from exact anchor evaluations, validates predictions selectively, and evaluates a shortlist exactly.
Source: §IV · p. 4, B. Grouping and Anchor Selection · p. 5Results
3.17× in sticking mode and 2.53× in walking mode, CTCS speeded evaluation while closely matching exhaustive evaluation's mean objective in both modes.
Source: B. Selection Quality and Computational… · p. 7Takeaways & Limitations
The benefit of environmental contact depends on the selected surface and configuration, and task-dependent selection outperformed the tested fixed-contact baseline.
Source: §VI · p. 8CTCS selects from sampled candidates, so global optimality over continuous contact locations and configurations is not guaranteed.
Source: §VI · p. 8
Abstract
from arXiv · showhide
In this paper, we study the joint selection of an environmental support contact and a whole-body configuration for a prescribed loco-manipulation task. A contact may provide greater physical support while restricting the motion required for the task. We formulate this problem through three capability measures: residual wrench, end-effector reach, and base mobility available after satisfying the task requirements, and we balance them against contact acquisition cost. Evaluating these capabilities for every candidate requires repeated whole-body optimizations. To reduce this computational cost, we propose Capability-Tradeoff Contact Selection (CTCS). CTCS screens candidates for contact and task feasibility, groups similar candidates within each surface, and predicts their capabilities from exact anchor evaluations using local sensitivity analysis. It checks these predictions through selective exact evaluations, ranks candidates by capability, and evaluates a shortlist exactly for final selection. We evaluate CTCS in simulations and hardware experiments using a Unitree Go2 quadruped with an AgileX NERO arm across $392$ task conditions with nine available support surfaces. Results show that CTCS outperforms ground-only and fixed-contact support, as it can select support surfaces that provide favorable capability trade-offs for the task. Compared with evaluating every candidate exactly, CTCS achieves approximately $3\times$ speedup while closely matching the resulting mean objective value.
I. INTRODUCTION
Environmental support can help legged mobile manipulators balance and perform demanding tasks, but the chosen contact also shapes the motion available for manipulation and locomotion. This paper treats the support realization as a task-dependent choice and introduces CTCS to evaluate candidates efficiently.
I. INTRODUCTION
- Long reaches or large end-effector wrenches challenge balance, while environmental support can help sustain the task but constrain required motion.The preferred support depends jointly on task load and motion requirements.Source: §I · p. 1
- CTCS screens task and contact feasibility, predicts capabilities from exact anchor evaluations within locally similar candidate groups, checks predictions selectively, and evaluates a shortlist exactly.The objective considers residual wrench, end-effector reach, and base mobility while accounting for contact acquisition cost.Source: §I · pp. 1–2
A. Environmental Contacts for Whole-Body Support
- Prior work uses environmental contacts for support and performance, while contact-planning methods select footholds or contacts during locomotion and trajectory planning.The paper distinguishes selecting a sustained auxiliary support for a given task from planning contact sequences or trajectories.Source: A. Environmental Contacts for… · p. 2, B. Contact Selection · p. 2
B. Contact Selection
- The paper jointly selects a sustained auxiliary support surface and the whole-body configuration that realizes it for a prescribed loco-manipulation task.The selection differs from assuming a support surface or type in advance and optimizing how to use it.Source: §I · p. 1, B. Contact Selection · p. 2
C. Efficient Evaluation of Contact Candidates
Evaluating capabilities across many support candidates is costly and local predictions may be unreliable across active-constraint or surface changes. The paper introduces the robot and environmental-contact representation used to pose this evaluation problem.
C. Efficient Evaluation of Contact Candidates
- Many surface and configuration candidates require repeated whole-body optimization, while active torque or friction constraints can change capability nonsmoothly and undermine local predictions.The candidates span discrete surfaces with different geometric and contact constraints.Source: C. Efficient Evaluation of Contact… · p. 2
III. PRELIMINARIES AND PROBLEM FORMULATION
- The modeled robot is a quadruped mobile manipulator with base position and orientation, leg and arm joints, and whole-body dynamics driven by actuation and contact forces.The dynamics include stance-foot and environmental contact forces as well as an end-effector wrench.Source: §III · pp. 2–3
A. Definition of Environmental Contacts
- A candidate contact realization pairs a robot configuration with an environmental surface and must meet geometric, usable-region, and contact-mode conditions.Sticking requires zero contact-point velocity; sliding permits tangential velocity and uses kinetic friction opposing it.Source: A. Definition of Environmental Contacts · p. 3
B. Task Requirements and Capability Measures
Task feasibility requires the prescribed task quantities to be supported across stance phases. Capability measures describe the remaining wrench, end-effector reach, and—in walking tasks—base mobility available around those requirements.
B. Task Requirements and Capability Measures
- A candidate must support the required end-effector wrench and task values, with feasibility maintained across the specified stance phases.The stance set includes two diagonal trot phases for walking and four-foot stance for sticking-mode manipulation.Source: B. Task Requirements and Capability… · p. 3
- Residual wrench capability measures additional feasible wrench variation while required end-effector position and base velocity are maintained.The measure uses a conservative inner approximation of the residual wrench region and its largest origin-centered ball.Source: B. Task Requirements and Capability… · p. 3
- Residual end-effector reach capability measures feasible position variation around the required position while sustaining the required wrench.The local displacement measure uses a fixed short horizon and task-aligned position axes.Source: B. Task Requirements and Capability… · p. 3
- For walking, residual base mobility measures feasible velocity variation along the prescribed base-motion direction; each capability uses its weakest stance phase.The mobility component is omitted for sticking-mode manipulation, and a zero directional reserve sets its corresponding capability to zero.Source: B. Task Requirements and Capability… · pp. 3–4
C. Problem of Interest
The selection objective favors feasible contacts and configurations with greater residual capabilities and lower acquisition cost. Exact capability evaluation is expensive, and a global approximation can be unreliable when constraints change.
C. Problem of Interest
- Among candidates satisfying contact and task conditions, the objective balances task-weighted residual capabilities against the weighted cost of transitioning from the current configuration.The capability vector contains task-applicable measures.Source: C. Problem of Interest · p. 4
- Evaluating every candidate requires many whole-body optimizations, and nearby candidates can have nonsmooth capability changes when active torque, friction, or contact constraints differ.The candidate set may grow to explore high-dimensional configuration space across environmental surfaces.Source: C. Problem of Interest · p. 4
IV. METHODOLOGY
CTCS reduces the cost of evaluating candidate support configurations by combining exact feasibility screening with selective capability evaluation. It predicts capabilities locally from exact evaluations and finishes with exact evaluation of a shortlist.
IV. METHODOLOGY
- Exact evaluation of every candidate requires many whole-body optimizations across task-applicable capabilities and stance phases.Source: §IV · p. 4
- CTCS combines exact feasibility screening, local sensitivity-based capability prediction, and selective exact evaluation.The method targets the repeated whole-body optimizations required to evaluate every candidate's capability vector.Source: §IV · p. 4
- CTCS screens candidates, groups survivors by realization and contact Jacobian, and uses an evaluated group representative to predict nearby candidates' capabilities.The predictions are validated before the top-ranked candidates receive exact evaluation for final selection.Source: §IV · p. 4
A. Candidate Generation and Task Feasibility Screening
The method samples a finite set of contact configurations for each surface, realizes them as whole-body configurations, and retains candidates that satisfy contact and task feasibility.
A. Candidate Generation and Task Feasibility Screening
- For each surface, the method samples manipulator joints, base position, base roll and pitch, and foothold locations within bounds.These sampled quantities form the candidate coordinates θ.Source: A. Candidate Generation and Task… · p. 4
- The sampled coordinates determine whole-body configurations, with bounds chosen to avoid leg and manipulator singularities and keep the realization locally differentiable.Configurations failing contact conditions are filtered out until N candidates are retained.Source: A. Candidate Generation and Task… · p. 4
- Each retained candidate pairs a whole-body configuration q_j with its environmental contact surface Π_j.Source: A. Candidate Generation and Task… · p. 4
- Candidates are screened against task-feasibility condition (T1) in every stance phase, and only those passing all phases proceed.Source: A. Candidate Generation and Task… · p. 4
B. Grouping and Anchor Selection
CTCS groups candidates by both their whole-body realization and contact mapping, then selects an exactly evaluated anchor when local modeling conditions are met.
B. Grouping and Anchor Selection
- Grouping by surface alone is insufficient because different realizations on one surface can induce different actuation, friction, and active constraints.Source: B. Grouping and Anchor Selection · p. 4
- Groups are formed separately on each surface using realization coordinates θ and contact Jacobians Jc(q), which capture configuration and contact-mapping differences.Complete-linkage clustering uses a maximum group diameter to bound within-group differences.Source: B. Grouping and Anchor Selection · p. 5
- Candidates are tested from the group center outward, and an anchor is accepted only when exact directional capability solutions satisfy the stated regularity and reserve conditions.Centrality is measured by each candidate's maximum distance to other group members.Source: B. Grouping and Anchor Selection · p. 5
- If no group member meets the anchor conditions, CTCS evaluates every member of that group exactly instead of constructing a local model.Source: B. Grouping and Anchor Selection · p. 5
C. Anchor-based Prediction, Validation, and Selection
CTCS predicts group members' capabilities from an anchor's local sensitivity, validates those predictions, and exactly evaluates a ranked shortlist before selection.
C. Anchor-based Prediction, Validation, and Selection
- An anchor's local sensitivity supports first-order capability predictions for nearby group members, but does not guarantee accuracy throughout the group.The realization equations make q locally differentiable in θ, and the sensitivity is obtained through the implicit function theorem.Source: C. Anchor-based Prediction,… · p. 5
- The method predicts capability reserves from anchor values and local gradients, then forms each capability from positive-negative reserve pairs and takes the minimum across stance phases.Source: C. Anchor-based Prediction,… · p. 5
- A probe exactly evaluates the group member farthest from its anchor; excessive prediction error triggers regrouping at half the diameter, and groups failing again are evaluated exactly.Source: C. Anchor-based Prediction,… · p. 5
- A member close to another group's valid anchor receives a second prediction and is evaluated exactly if the predictions exceed a capability-specific tolerance.Source: C. Anchor-based Prediction,… · p. 5
- Candidates are ranked by estimated capability utility, and the shortlist receives exact capability evaluation before final selection.Shortlisted candidates satisfy the contact and task conditions and have exact capabilities for the selection objective.Source: C. Anchor-based Prediction,… · pp. 5–6
V. EXPERIMENTS AND RESULTS
The evaluation combines Gazebo simulations and hardware experiments on a quadruped mobile manipulator with nine selectable support surfaces. It tests sticking and walking tasks across varied end-effector force requirements and compares CTCS with baselines and ablations.
V. EXPERIMENTS AND RESULTS
- The study evaluates CTCS in Gazebo simulations and hardware experiments.The experiments assess contact-selection quality, computational cost, and task performance against baselines.Source: §V · p. 6
- A Unitree Go2 with an AgileX NERO 7-DoF arm selects among nine 5 m support surfaces and multiple whole-body configurations.The surfaces comprise one vertical wall, four tables, and four horizontal rails at different heights.Source: §V · p. 6
- The evaluation covers 392 task conditions: 196 each for sticking and walking, varying force direction and magnitude from 5 to 70 N.Walking tasks require a base velocity of 0.1 m/s along the support surface.Source: §V · p. 6
- Candidate generation yields 45,000 sampled candidates, of which an average of 27,851 satisfy the task-feasibility condition across the 392 tasks.The candidates are sampled per surface after satisfying contact and configuration constraints.Source: §V · p. 6
- Comparisons include exhaustive evaluation, ground-only search, fixed contact, and ablations of prediction validation, candidate grouping, and the walking stance model.Table I reports certification rate, mean objective, selection agreement, runtime, and speedup over 196 conditions per mode.Source: §V · p. 6, Table I · p. 6
A. Environmental Contact Selection
In simulation, CTCS improves task certification and mean objective over ground-only and fixed-contact support, while approaching exhaustive evaluation with less computation. Its selected surfaces vary with task feasibility, friction, and geometry.
A. Environmental Contact Selection
- 91.8% of conditions were certified by CTCS in both modes, versus 68.4% in sticking and 65.3% in walking for ground-only search; mean objectives were 3.5419 versus 2.5324 and 5.6612 versus 3.9184, respectively.Uncertified conditions receive zero in the reported mean, so the objective comparison reflects both certification coverage and selected-candidate quality.Source: A. Environmental Contact Selection · p. 6
- Fixed-contact support certified 48.5% of sticking and 41.8% of walking conditions, with mean objectives of 2.1386 and 2.0812, below ground-only search on both metrics.The tested fixed candidate also fixes the whole-body configuration and contact geometry, which may not suit task requirements.Source: A. Environmental Contact Selection · p. 6
B. Selection Quality and Computational Cost
- CTCS reduced runtime from 124.0 s to 39.1 s in sticking and from 157.0 s to 62.1 s in walking, with 95.6% and 100% selection agreement with exhaustive evaluation, respectively.Mean objectives changed from 3.5428 to 3.5419 in sticking and remained 5.6612 in walking; removing prediction checks or local grouping lowered the mean objective.Source: B. Selection Quality and Computational… · pp. 6–7
C. Task-Dependent Environmental Structure Selection
- Feasible-candidate availability ranged from 10.6% to 12.1% in sticking and 9.9% to 12.0% in walking, while CTCS selection rates differed substantially across surfaces.Fig. 4 compares each surface’s share of feasible candidates with its selection rate.Source: C. Task-Dependent Environmental… · p. 7, Figure 4 · p. 7
- CTCS selected rails in 78.9% of certified walking conditions, most often the 0.265 m rail at 25.0%, while selecting the wall in only 3.9%.The authors suggest lower modeled kinetic friction on rails may reduce sliding friction, depending on contact normal forces.Source: C. Task-Dependent Environmental… · p. 7
- In sticking, selections were broader: the 0.31 m rail was most frequent at 22.2%, followed by the wall at 17.8%; preferences reflect friction, surface height, and task requirements.The wall’s higher modeled static friction is consistent with its greater use than in walking; surface height also affects configuration, joint effort, and margins to physical limits.Source: C. Task-Dependent Environmental… · p. 7
D. Hardware Experiments
Hardware trials demonstrate selected support contacts during sticking manipulation and walking, with low tracking errors reported across five trials. The conclusion notes that selection is limited to sampled candidates and does not guarantee global optimality.
D. Hardware Experiments
- Across five sticking-mode hardware trials, the robot maintained support while moving the end effector and sustaining a downward load; force and position RMSEs remained low.Without environmental support, the arm’s weight would cause the robot to roll over.Source: D. Hardware Experiments · p. 7
- Across five walking trials, the robot maintained sliding support while sustaining a load and tracking the prescribed base velocity and end-effector position.The greater end-effector position error than in sticking mode is attributed to body movement; the additional contact increases sustainable wrench but adds frictional resistance during locomotion.Source: D. Hardware Experiments · p. 7
- In a representative walking trial, wrist-reaction force followed the applied load, base velocity fluctuated around 0.1 m/s, and end-effector position error generally stayed below 30 mm.Remaining fluctuations are mainly attributed to alternating ground support and body motion during trot changes.Source: D. Hardware Experiments · p. 8, Figure 6 · p. 8
VI. CONCLUSION
- CTCS closely matched exhaustive evaluation’s mean objective with less computation, but sampled candidates do not guarantee global optimality over continuous contact locations and configurations.The conclusion identifies candidate refinement, contact transitions, and online reselection as future work.Source: §VI · p. 8