Estimating Dynamic Soft Continuum Robot States From Boundaries (2505.04491v1)

Abstract: Accurate state estimation is essential for effective control of robots. For soft robots, this task is particularly challenging because their states are inherently infinite-dimensional functions due to the robots' continuous deformability. Traditional sensing techniques, however, can only provide discrete measurements. Recently, a dynamic state estimation method known as a boundary observer was introduced, which leverages Cosserat rod theory to recover all infinite-dimensional states by measuring only the velocity twist at the robot's tip. In this work, we present a novel boundary observer that can also recover infinite-dimensional dynamic states, but instead relies on measuring the internal wrench at the robot's base. This design exploits the duality between the velocity twist at the tip and the internal wrench at the base, with both types of boundary observers being inspired by principles of energy dissipation. Despite the mathematical duality, the proposed approach offers a distinct advantage: it requires only a 6-axis force/torque sensor embedded at the base, eliminating the need for external sensing systems such as motion capture cameras. Moreover, combining both tip- and base-based techniques enhances energy dissipation, accelerates convergence, and improves estimation accuracy. We validate the proposed algorithms through both simulation studies and experiments based on tendon-driven continuum robots. Our results demonstrate that all boundary observers converge to the ground truth within 3 seconds, even with significantly deviated initial conditions. Furthermore, they recover from unknown perturbations and effectively track high-frequency vibrations. We also show that combining the dual techniques further improves convergence speed and accuracy. Finally, the computational efficiency of these algorithms indicates their feasibility for real-time state estimation.

The Shape Awakens: Estimating Dynamic Soft Robot States from the Outer Rim

The paper in question addresses the intricate problem of state estimation in the context of soft continuum robots. These robots exhibit infinite-dimensional state spaces due to their capacity for continuous deformation, posing substantial challenges to conventional sensing methods that typically deliver discrete data. The authors propose a boundary observer technique that innovatively combines measurements of internal wrenches at the robot's base with Cosserat rod theory to estimate the continuum robot's states.

The primary contribution is the novel boundary observer that uses a 6-axis force/torque (F/T) sensor at the robot's base, capitalizing on the duality between velocity and internal wrench. This approach contrasts with a previously known method, which required only tip velocity measurements. The base-based observer offers significant practical advantages, notably its independence from external sensing systems, making it particularly suited for small-scale applications and environments where external measurements are challenging to obtain. Furthermore, the method enhances energy dissipation properties, accelerates convergence, and improves estimation accuracy by integrating measurements from both the base and tip observers.

Analytical and Experimental Framework

The authors ground their approach in the mathematical framework of Cosserat rod theory, which models the robot’s state via nonlinear partial differential equations (PDEs). They derive the system dynamics and establish the necessary boundary conditions to allow the boundary observers to estimate the robot’s state. The base observer introduces energy dissipation-based correction terms, enhancing stability and convergence.

The dual observers—one at the tip and the other at the base—can be utilized collectively for improved performance. The synthesis of these two approaches brings forth a hybrid observer that benefits from the strengths of each, rendering it more accurate and rapidly converging than its component techniques alone.

The experimental validation, conducted on a tendon-driven continuum robot, demonstrates the efficacy of the proposed methods. All observer variants achieved convergence to the ground truth within three seconds from initialization, even with large initial deviations. The algorithms were shown to recover from unanticipated disturbances while maintaining high-frequency vibration tracking, a critical requirement for real-time dynamic state estimation. Additionally, the algorithm’s implementation in MATLAB achieved a real-time factor of operation, further underscoring its practicality for control applications.

Implications and Future Directions

The implications of this research are multifaceted. Practically, the observer system enhances the scope of control strategies available for dynamic continuum robots, dismissing the limitations of quasi-static assumptions and facilitating deployment in real-time applications without complex external sensor arrays. Theoretically, this work expands the understanding of dual approaches in state estimation, particularly within the field of infinite-dimensional systems modeled by PDEs.

Looking forward, the paper suggests a pathway towards integrating these algorithms directly into feedback control systems for continuum robots, potentially revolutionizing their efficacy in complex, dynamic tasks. Additionally, the framework set forth could be applied to develop further innovations in sensor and actuator design for soft robotics, pushing the boundaries of where and how these systems can be effectively utilized.