State and Trajectory Estimation of Tensegrity Robots via Factor Graphs and Chebyshev Polynomials

2026-04-09

AI Summary

This work addresses the challenge of state estimation in tensegrity robots, which arises from their highly nonlinear and under-constrained dynamics. To tackle this problem, the authors propose a two-stage continuous-time state estimation algorithm based on factor graph optimization. The method fuses RGB-D camera data with cable length measurements and represents the first application of factor graph optimization to this class of robots. It incorporates Mahalanobis distance-based clustering to suppress sensor noise and employs Chebyshev polynomial interpolation to achieve high-fidelity estimation of intermediate states and velocities. Experimental results demonstrate that the proposed approach significantly outperforms baseline methods such as ICP in both simulation and real-world scenarios, enabling accurate, continuous-time trajectory reconstruction even during complex motions.

Abstract

Tensegrity robots offer compliance and adaptability, but their nonlinear, and underconstrained dynamics make state estimation challenging. Reliable continuous-time estimation of all rigid links is crucial for closed-loop control, system identification, and machine learning; however, conventional methods often fall short. This paper proposes a two-stage approach for robust state or trajectory estimation (i.e., filtering or smoothing) of a cable-driven tensegrity robot. For online state estimation, this work introduces a factor-graph-based method, which fuses measurements from an RGB-D camera with on-board cable length sensors. To the best of the authors' knowledge, this is the first application of factor graphs in this domain. Factor graphs are a natural choice, as they exploit the robot's structural properties and provide effective sensor fusion solutions capable of handling nonlinearities in practice. Both the Mahalanobis distance-based clustering algorithm, used to handle noise, and the Chebyshev polynomial method, used to estimate the most probable velocities and intermediate states, are shown to perform well on simulated and real-world data, compared to an ICP-based algorithm. Results show that the approach provides high fidelity, continuous-time state and trajectory estimates for complex tensegrity robot motions.

Problem

• tensegrity robots
• state estimation
• trajectory estimation
• nonlinear dynamics
• underconstrained systems

Innovation

• factor graphs
• Chebyshev polynomials
• tensegrity robots
• state estimation
• sensor fusion