Multi-Contact Force Estimation for Continuum Robots via Gaussian-Parameterized Factor Graphs

2026-06-27

AI Summary

This work addresses the challenge of accurately estimating external contact forces at arbitrary locations along continuum robots operating in unstructured environments, a task complicated by the ill-posed nature of simultaneously identifying both the location and magnitude of multi-point contacts. To tackle this issue, the authors propose a joint shape-and-force estimation framework grounded in a probabilistic Cosserat rod model. The approach integrates strain, tendon tension, and pose measurements within a factor graph formulation and employs a Gaussian mixture model to parameterize contact forces, thereby reducing the dimensionality of unknown forces and mitigating ill-posedness. A progressive variant is further introduced, enabling sequential, on-demand activation of basis functions during constrained navigation tasks to enhance computational efficiency. Simulations demonstrate that the method outperforms existing approaches in estimating both the location and magnitude of contact forces under single- and multi-point contact scenarios.

Abstract

Continuum robots offer key advantages in navigating unstructured environments, but their safe operation requires accurate estimation of the external contact forces acting anywhere along the robot body. Estimating these forces at unknown locations is an ill-conditioned problem, particularly for multiple contacts. We propose a unified shape and force estimation framework formulated on a factor graph. By incorporating a Gaussian mixture force parameterization into a discretized probabilistic Cosserat rod model, we reduce the dimensionality of the unknown external forces and mitigate the ill-conditioning of node-wise force estimation. The framework fuses strain, tendon tension, and pose measurements to simultaneously estimate the robot's shape and external forces while accounting for modeling and sensor uncertainties. Numerical simulations demonstrate that the proposed method outperforms existing methods in terms of force location and magnitude estimation for both single and multi-contact scenarios. We further present a progressive variant that introduces basis functions on demand to estimate contact forces sequentially during a simulated confined-navigation task.

Problem

• Continuum robots
• Multi-contact force estimation
• Ill-conditioned problem
• External contact forces
• Force location

Innovation

• Gaussian mixture parameterization
• factor graph
• continuum robot
• multi-contact force estimation
• probabilistic Cosserat rod model