Towards Contact-Aided Motion Planning for Tendon-Driven Continuum Robots

TL;DR

This work proposes a search-based motion planner for a single-segment TDCR, guided by a specially designed heuristic that provides an effective cost-to-go estimation while respecting the kinematic constraints of the TDCR and environmental interactions.

Abstract

Tendon-driven continuum robots (TDCRs), with their flexible backbones, offer the advantage of being used for navigating complex, cluttered environments. However, to do so, they typically require multiple segments, often leading to complex actuation and control challenges. To this end, we propose a novel approach to navigate cluttered spaces effectively for a single-segment long TDCR which is the simplest topology from a mechanical point of view. Our key insight is that by leveraging contact with the environment we can achieve multiple curvatures without mechanical alterations to the robot. Specifically, we propose a search-based motion planner for a single-segment TDCR. This planner, guided by a specially designed heuristic, discretizes the configuration space and employs a best-first search. The heuristic, crucial for efficient navigation, provides an effective cost-to-go estimation while respecting the kinematic constraints of the TDCR and environmental interactions. We empirically demonstrate the efficiency of our planner-testing over 525 queries in environments with both convex and non-convex obstacles, our planner is demonstrated to have a success rate of about 80% while baselines were not able to obtain a success rate higher than 30%. The difference is attributed to our novel heuristic which is shown to significantly reduce the required search space.

Figures (5)

• Figure 1: (a) Problem statement: the end-effector of a TDCR must reach a given target pose in a cluttered environment, (b) Single-segment TCDR's unsuccessful solution (without CAN) which intersects an obstacle, (c) Three-segment TDCR's successful solution, (d) Single-segment's successful solution (with CAN) obtained by leveraging the obstacles to vary its curvature and reach the target pose.
• Figure 2: (a) Robot shape at $\mathbf{q}_{\mathrm{init}}$ and at $\mathbf{q}_{\mathrm{init}}+\sigma$ with respective end-effector positions. (b) Workspace $\mathcal{W}\xspace$ with obstacles indicated in blue. The backbone is represented by a sequence of constant-curvature arcs subtending an angle $\theta_i$ with curvatures $\kappa_i$, where $i=1,\ldots,m$. The tendons are indicated in violet.
• Figure 3: (a) Robot's initial configuration at $\mathbf{q}$. (b), (c) Overlayed robot shapes for joint sequences (b) $\sigma$ (two length-extensions, and three bending actions) and (c) $\sigma'$ (reverse order: three bending actions, and two length-extensions).
• Figure 4: Diagrammatic representation of the heuristic calculation. (a) PopulateCCArcs$\left(\mathbf{p}\textsubscript{goal}, \psi_{goal}\right)$ evaluates cell poses that contain CC arcs (red) to reach a goal pose. Note that from each cell pose, only one arc reaches the goal. (b) Having obstacles (blue) invalidates some of the CC arcs. Running IdenitfyContact(cell) for each cell pose identified in the previous step identifies contact cells (green circles). (c) Using one of the contact cells, cell $c$, PopulateCCArcs$\left(\mathbf{p}\textsubscript{c}, \psi_{c}\right)$ is run, identifying new CC arcs that reach its pose (green) (d) After the above steps, we can see (i) positions from which arcs with several orientations were computed (e.g., cell $b$ and cell $a$) and (ii) For the illustrated robot, the proposed heuristic informs the planner that based on its current end-effector orientation it can reach the goal via the CC arc connecting cell $a$ and $c$, and consequently $c$ to the goal.
• Figure 5: Comparison of our motion planner $\mathcal{M}_{\text{CAN}}$ with the BFS planner used to generate the queries across three workspaces. For each plot we report (Top right) a heatmap showing the number of successful solutions for both BFS (y-axis) and $\mathcal{M}_{\text{CAN}}$ (x-axis), with numerical counts displayed within each cell. (Bottom right) $N_{\text{xp}}$, the average nodes expanded ($\times1e3$ for $\mathcal{M}_{\text{CAN}}$ (purple) and BFS (grey)) with increasing number of contacts. Please note that the y-axis scale differs between the two planners.