A bioinspired internal model-based online estimator for planar pursuit

Tengyue Liu, Xincheng Li, Sofia Morales Ferreira, Kevin Galloway, Udit Halder · N/A · 2026

Summary

Bioinspired feedback controls for pursuit, tracking, and collective motion are often expressed in terms of the relative configuration between interacting agents.

Abstract Summary

Bioinspired feedback controls for pursuit, tracking, and collective motion are often expressed in terms of the relative configuration between interacting agents. In practice, however, onboard sensors may not directly provide all quantities required for feedback control, necessitating estimation of unobserved quantities. This paper develops a bioinspired internal model-based estimator for reconstructing those quantities from partial sensory observations and known self-motion. State reconstruction is posed as an optimization problem that treats the relative kinematics as constraints and minimizes the disagreement between the internal model outputs and measurements from onboard sensors. Pontryagin's Maximum Principle is used to derive the necessary optimality conditions. A forward-backward algorithm is used to provide a numerical solution and a moving horizon formulation is employed for online implementation. The estimator is evaluated numerically against classical state estimators. Real-time implementation of the proposed framework on robotic hardware is demonstrated through two pursuit strategies.

Key Points

Bioinspired feedback controls for pursuit, tracking, and collective motion are often expressed in terms of the relative configuration between interacting agents.
In practice, however, onboard sensors may not directly provide all quantities required for feedback control, necessitating estimation of unobserved quantities.
This paper develops a bioinspired internal model-based estimator for reconstructing those quantities from partial sensory observations and known self-motion.
State reconstruction is posed as an optimization problem that treats the relative kinematics as constraints and minimizes the disagreement between the internal model outputs and measurements from onboard sensors.
Pontryagin's Maximum Principle is used to derive the necessary optimality conditions

Preliminaries

Consider two agents moving in the plane spanned by the global inertial frame $\{\mathbf{e}_{1},\mathbf{e}_{2}\}$ (see Fig. 1 (a)).

Agent $i$ has global position $\mathbf{r}_{i}=x_{i}\,\mathbf{e}_{1}+y_{i}\,\mathbf{e}_{2}$ and heading $\theta_{i}$ that describes the moving frames $\mathbf{x}_{i}=\cos\theta_{i}\,\mathbf{e}_{1}+\sin\theta_{i}\,\mathbf{e}_{2}$ and $\mathbf{y}_{i}=-\sin\theta_{i}\,\mathbf{e}_{1}+\cos\theta_{i}\,\mathbf{e}_{2}$.

Preliminaries — A bioinspired internal model-based online estimator for planar pursuit — Fig. 1: Two-agent formation. (a) The agents evolve in the global inertial frame $\{\mathbf{e}_{1},\mathbf{e}_{2}\}$, with their relative configuration described by the shape variables $(\rho,\alpha_{1},\alpha_{2})$. (b) In the body-fixed frame $\{\mathbf{x}_{2},\mathbf{y}_{2}\}$ attached to agent 2, the relative configuration of agent 1 is described by the coordinates $(x,y,\theta)$.

Internal Model-based Estimator (IME)

In this section, we propose an internal model-based estimator (IME) which uses partial observations to reconstruct the relative states and unknown controls of the pursuee required for feedback. We suppose that pursuer maintains an internal representation of the relative state $z$ and pursuee controls $\eta_{1}$.

Numerical and Experimental Results

Numerical simulations and physical experiments are used to quantify both estimation accuracy and control execution of the proposed estimator. The code used for all simulations and experiments is available at [ 31 ] . While the proposed estimator is applicable to any feedback control laws of the form ( 6 ), this paper focuses on two specific bioinspired pursuit strategies for the evaluation.

A brief introduction to these pursuit strategies is provided next. Shape variables.

Numerical and Experimental Results — A bioinspired internal model-based online estimator for planar pursuit — Fig. 5: Top view of the TurtleBot3 Burger (side view in the inset) showing the dual LiDAR configuration. The effective fields of view (FOVs) of the front and rear LiDARs are shown in blue and orange, respectively.

Sources and Demonstrations

Figures are reproduced from Liu et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.