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.

翻译：张拉整体机器人具有顺应性和适应性，但其非线性、欠约束的动力学特性使得状态估计面临挑战。对闭合控制、系统辨识及机器学习而言，可靠的所有刚性连杆连续时间估计至关重要，然而传统方法往往表现不足。本文提出一种两阶段方法，用于实现缆索驱动张拉整体机器人的鲁棒状态或轨迹估计（即滤波或平滑）。在在线状态估计方面，本研究引入了一种基于因子图的方法，该方法融合了RGB-D相机与机载缆索长度传感器的测量数据。据作者所知，这是因子图在该领域的首次应用。因子图是一种自然而然的优选方法，因为它利用了机器人的结构特性，并提供了能够实际处理非线性的有效传感器融合方案。与基于ICP的算法相比，基于马氏距离的聚类算法（用于处理噪声）和切比雪夫多项式方法（用于估计最可能的速度与中间状态）在模拟和真实数据上均表现出良好性能。结果表明，该方法能够为复杂的张拉整体机器人运动提供高保真度、连续时间的状态与轨迹估计。