Abstract-- This work demonstrates pose (position and shape) estimation for a free-floating, bioinspired multi-link robot with unactuated joints, link-mounted thrusters for control, and a single gyroscope per link, resulting in an underactuated, minimally sensed platform. Through a proof-of-concept hardware experiment and offline Kalman filter analysis, we show that the robot's pose can be reliably estimated. State estimation is performed using an unscented Kalman filter augmented with Gaussian process residual learning to compensate for nonzero-mean, non-Gaussian noise. We further show that a filter trained on a multi-gait dataset (forward, backward, left, right, and turning) performs comparably to one trained on a larger forward-gait-only dataset when both are evaluated on the same forward-gait test trajectory. These results reveal overlap in the gait input space, which can be exploited to reduce training data requirements while enhancing the filter's generalizability across multiple gaits. I. Introduction The performance of dynamical systems such as underwater robots, autonomous vehicles, and aircraft autopilots critically depends on accurate knowledge of the system state to ensure robustness against disturbances and maintain safety guarantees. At the same time, size, weight, and power constraints limit the number and type of sensors and actuators that can be incorporated into many systems, leading to systems that are both underactuated and minimally sensed.

This work is motivated by the development of cooperative teams of small, soft underwater robots designed to accomplish complex tasks through collective behavior. These robots take inspiration from biology: salps are gelatinous, jellyfish-like marine animals that utilize jet propulsion for maneuvering and can physically connect to form dynamic chains of arbitrary shape and size. The primary contributions of this research are twofold: first, we adapt a planar nonlinear multi-link snake robot model to model a planar multi-link salp-inspired system by removing joint actuators, introducing link thrusters, and allowing for non-uniform link lengths, masses, and moments of inertia. Second, we conduct a nonlinear observability analysis of the multi-link system with link thrusters, showing that the link angles, angular velocities, masses, and moments of inertia are locally observable when equipped with inertial measurement units and operating under specific thruster conditions. This research provides a theoretical foundation for modeling and estimating both the state and intrinsic parameters of a multi-link system with link thrusters, which are essential for effective controller design and performance.