Tensegrity Robot Proprioceptive State Estimation with Geometric Constraints

TL;DR

This work addresses the challenge of dead-reckoning for tensegrity robots by introducing a proprioceptive state estimator that combines a constrained shape-reconstruction module with a contact-aided Right Invariant EKF. The method first reconstructs the body-frame endcap geometry from cable lengths and IMU data, then uses forward kinematics within a RI-EKF to estimate global pose, achieving an average drift of approximately $4.2\%$ over real-world and simulated trajectories. Key contributions include the first proprioceptive InEKF capable of estimating both shape and pose for a tensegrity robot, and a geometry-based optimization that enforces tensegrity constraints (rod lengths, chirality, and non-crossing) to improve shape accuracy. The approach runs in real time on onboard sensors, enabling autonomous operation in unstructured environments and advancing the practical deployment of tensegrity systems.

Abstract

Tensegrity robots, characterized by a synergistic assembly of rigid rods and elastic cables, form robust structures that are resistant to impacts. However, this design introduces complexities in kinematics and dynamics, complicating control and state estimation. This work presents a novel proprioceptive state estimator for tensegrity robots. The estimator initially uses the geometric constraints of 3-bar prism tensegrity structures, combined with IMU and motor encoder measurements, to reconstruct the robot's shape and orientation. It then employs a contact-aided invariant extended Kalman filter with forward kinematics to estimate the global position and orientation of the tensegrity robot. The state estimator's accuracy is assessed against ground truth data in both simulated environments and real-world tensegrity robot applications. It achieves an average drift percentage of 4.2%, comparable to the state estimation performance of traditional rigid robots. This state estimator advances the state of the art in tensegrity robot state estimation and has the potential to run in real-time using onboard sensors, paving the way for full autonomy of tensegrity robots in unstructured environments.

Figures (12)

• Figure 1: Tensegrity robot state estimation experiment setup, the robot is teleoperated to roll on flat ground.
• Figure 2: Tensegrity robot structure and coordination frames. Orientation $\mathbf{R}_t$ and position $\mathbf{p}_t$ of the robot are represented with respect to the world frame ($\mathbf{W}$). The IMU measurements $\mathbf{a}_t$, $\mathbf{\omega}_t$ are in the IMU frame, which is aligned with the Body frame ($\mathbf{B}$).
• Figure 3: Tensegrity robot state estimation framework. Firstly, the real-world or simulated IMU and cable length sensors are input into an optimization-based robot shape reconstruction algorithm, as discussed in Sec. \ref{['sec: optimization']}. The reconstructed shape provides the positions of the robot's endcaps in the body frame. Next, the computed kinematics, based on the contact points between the endcaps and ground, are utilized within a contact-aided Invariant EKF to estimate the robot pose. Finally, the global endcap positions are computed by transforming the reconstructed shape into the body pose within a global frame.
• Figure 4: Illustration of 3-bar tensegrity robot chirality from side-view. The right configuration is twisting counter-clockwise, the same structure we used in simulation and real-world robots.
• Figure 5: Illustration of geometric constraints, red arrows represent the vectors chained to each rod center, blue arrows represent their cross-product vectors. In the left figure, the geometric constraints are satisfied, with the cross-product vector pointing along the robot's axial direction to the right. Conversely, the right figure demonstrates a switch to the opposite direction. The endcap colors in the circled area follow yellow-green-pink in the left figure and yellow-pink-green in the right, demonstrating the difference in the robot configuration.