Shape-Space Graphs: Fast and Collision-Free Path Planning for Soft Robots

TL;DR

This work addresses fast, collision-free path planning for soft robots whose continuum kinematics are nonlinear and infinite-dimensional. It introduces a shape-space roadmap built from a morphoelastic, active-filament model of a three-fiber elephant-trunk-inspired arm, with an offline shape library and a $k$-NN graph that guarantees physically valid shapes. Collision avoidance is achieved with obstacle-SDF pruning and a multi-objective edge-cost that trades geometric proximity against actuation energy and smoothness, solved by Dijkstra's algorithm in milliseconds. The results show substantial reductions in actuation effort when energy costs are included, at the cost of slightly longer tip trajectories, demonstrating potential for real-time surgical, industrial, and assistive applications.

Abstract

Soft robots, inspired by elephant trunks or octopus arms, offer extraordinary flexibility to bend, twist, and elongate in ways that rigid robots cannot. However, their motion planning remains a challenge, especially in cluttered environments with obstacles, due to their highly nonlinear and infinite-dimensional kinematics. Here, we present a graph-based path planning tool for an elephant-trunk-inspired soft robotic arm designed with three artificial muscle fibers that allow for multimodal continuous deformation through contraction. Using a biomechanical model inspired by morphoelasticity and active filament theory, we precompute a shape library and construct a $k$-nearest neighbor graph in \emph{shape space}, ensuring that each node corresponds to a mechanically accurate and physically valid robot shape. For the graph, we use signed distance functions to prune nodes and edges colliding with obstacles, and define multi-objective edge costs based on geometric distance and actuation effort, enabling energy-efficient planning with collision avoidance. We demonstrate that our algorithm reliably avoids obstacles and generates feasible paths within milliseconds from precomputed graphs using Dijkstra's algorithm. We show that including energy costs can drastically reduce the actuation effort compared to geometry-only planning, at the expense of longer tip trajectories. Our results highlight the potential of shape-space graph search for fast and reliable path planning in the field of soft robotics, paving the way for real-time applications in surgical, industrial, and assistive settings.

Figures (4)

• Figure 1: Shape-space graphs: We use a biomechanical model of our three-fiber soft robotic arm inspired by the elephant’s muscular structure to precompute a large shape library paired with corresponding fiber activation tuples. Constructing a $k$-nearest neighbor graph in the robot's shape space ($\mathcal{S}$-space) transforms the path planning problem into a graph search, enabling efficient multi-objective optimization that minimizes activation effort while avoiding obstacles.
• Figure 2: Three-fiber soft robotic arm kaczmarski2024Minimalleanza2024Elephant: The orientation of the fibers is inspired by the muscular structure of the elephant trunk, with one straight fiber and a helical fiber pair, enabling continuous deformations and great reachability.
• Figure 3: Sequence of shapes $\bm{r}(z)$ (top) and activations $\bm{\gamma}$ (bottom) of the box obstacle scenario for two different edge cost formulations. Shapes are color-coded according to progression along the robot’s path segments. Activations $\gamma_i$ are depicted for each fiber to compare in between the edge cost formulations.
• Figure 4: Sequence of shapes $\bm{r}(z)$ (top) and activations $\bm{\gamma}$ (bottom) of the cylinder obstacle scenario with multiple waypoints and for two different edge cost formulations. Shapes are color-coded according to progression along the robot’s path segments. Activations $\gamma_i$ are depicted for each fiber to compare in between the edge cost formulations, for normed path segments.