Contact Modes Are Strata: What Geometric Structure Buys in Discrete-Continuous Planning

Phone Thiha Kyaw; Jonathan Kelly

cs.ROAug 16, 2026

Contact Modes Are Strata: What Geometric Structure Buys in Discrete-Continuous Planning

Authors: Phone Thiha Kyaw, Jonathan Kelly

Organizations: Space and Terrestrial Autonomous Robotic Systems (STARS) Laboratory University of Toronto Institute for Aerospace Studies (UTIAS) Toronto, Ontario M3H 5T6, Canada

Abstract

Contact-rich manipulation poses a discrete question and a continuous one at once, namely which contacts are active and how to move while they hold. The two are coupled by a change of dimension, since each contact that a robot maintains confines its motion to a lower-dimensional manifold. We make that coupling the explicit object of planning by observing that a contact mode is not merely analogous to a stratum of the configuration space; it is one. A plan is then a walk over strata whose within-stratum segments are geodesics. On two contact-rich manipulation tasks in simulation, pushing a T-shaped block around obstacles and reorienting a cube in a dexterous hand, our planner returns solutions within seconds with no mode, contact sequence, or stratum given in advance.

Figures & tables

Fig. 2 : Contacts stratify the configuration space of a point robot between a floor and a wall (

n=2

). (a) Each signed distance gives the gap to one surface and vanishes where the robot touches it. (b) Grouping configurations by which distances vanish gives four strata, of dimension

n-|A|

. (c) A hybrid path

\sigma

lies within strata and crosses between them where one contact is made or broken (diamonds). (d) The same crossings on the stratum graph, numbered as in (c), where making a contact raises the codimension by one and breaking one lowers it.

Fig. 3 : One plan per task, drawn as a walk over strata. We plot the number of active contacts

|A|

, which fixes the stratum’s codimension by ( 2 ), against path length, with filled triangles making a contact and open ones breaking one. Pushing the block past an obstacle cannot be done from one face, so the walk returns to free space and approaches again. Turning the cube cannot be done from a fixed grasp at all, and the walk becomes a gait.

	$n$	solved	time	make/break
T-shaped block	10	48/48	760 ms	5 / 4
Cube in hand	19	48/48	9.9 s	52 / 52

TABLE I : Results over 48 trials per task on a single CPU core.

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Continuum robots are well suited for navigating confined and fragile environments, such as vascular or endoluminal anatomy, where contact with surrounding structures is often unavoidable. While controlled contact can assist motion, unfavorable contact can degrade controllability, induce kinematic singularities, or introduce safety risks. We present a contact-aware planning approach that evaluates contact quality, penalizing hazardous interactions, while permitting benign contact. The planner produces kinematically feasible trajectories and contact-aware Jacobians which can be used for closed-loop control in hardware experiments. We validate the approach by testing the integrated system (planning, control, and mechanical design) on anatomical models from patient scans. The planner generates effective plans for three common anatomical environments, and, in all hardware trials, the continuum robot was able to reach the target while avoiding dangerous tip contact (100% success). Mean tracking errors were 1.9 +/- 0.5 mm, 1.2 +/- 0.1 mm, and 1.7 +/- 0.2 mm across the three different environments. Ablation studies showed that penalizing end-of-continuum-segment (ECS) contact improved manipulability and prevented hardware failures. Overall, this work enables reliable, contact-aware navigation in highly constrained environments.

Abstract

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