A bioinspired internal model-based online estimator for planar pursuit

In many biological and engineered pursuit scenarios, agents must track a target using only relative sensory information (like distance and bearing). However, standard feedback control laws often require knowledge of the target's full state and motion commands, which are rarely directly observable. This paper addresses the problem of reconstructing these unobserved quantities in real-time to enable effective pursuit.

Inspired by the biological hypothesis that nervous systems maintain internal models of their environment, the authors propose an Internal Model-based Estimator (IME). Instead of using traditional filtering (like an Extended Kalman Filter), the IME treats state reconstruction as a dynamic optimization problem. It maintains an internal model of the target's kinematics and optimizes the estimated trajectory to minimize the disagreement between the internal model's predicted outputs and the actual sensor measurements. The authors use Pontryagin's Maximum Principle (PMP) to derive the optimality conditions and implement the solution using a forward-backward algorithm within a moving-horizon framework for online performance.

Numerical simulations and robotic experiments demonstrate that the IME outperforms traditional estimators like the Extended Kalman Filter (EKF) and Particle Filter (PF) in both estimation accuracy and sensitivity to initial guesses. The IME successfully reconstructs the target's time-varying linear and angular speeds, enabling the pursuer to execute complex strategies such as constant-bearing pursuit and mutual motion camouflage. The framework was successfully validated on physical TurtleBot3 robots, showing that it can reliably guide pursuit even when the target's control inputs are unknown.

This work bridges the gap between theoretical geometric control and practical robotic implementation. By providing a robust way to estimate unobserved target dynamics, the IME enables autonomous agents to perform sophisticated, bioinspired maneuvers in real-world environments where full state information is unavailable. It offers a flexible, optimization-based alternative to traditional state observers that struggle with unknown, time-varying target controls.