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On-line Motion Planning Using Bernstein Polynomials for Enhanced Target Localization in Autonomous Vehicles

Camilla Tabasso, Venanzio Cichella

TL;DR

The paper tackles online motion planning for target localization by a single autonomous vehicle under motion and safety constraints. It introduces a Bernstein-polynomial framework to represent both the vehicle trajectory and the target's probability distribution, embedding estimation performance via the determinant of the Fisher Information Matrix into a multi-objective NLP. Key contributions include a Bernstein approximation of the OCP with degree elevation, de Casteljau-based evaluation, and Bernstein-estimated PDF, with simulations showing that maximizing information yields faster and more accurate localization. The approach enables real-time, single-vehicle target localization across diverse sensing models and environments.

Abstract

The use of autonomous vehicles for target localization in modern applications has emphasized their superior efficiency, improved safety, and cost advantages over human-operated methods. For localization tasks, autonomous vehicles can be used to increase efficiency and ensure that the target is localized as quickly and precisely as possible. However, devising a motion planning scheme to achieve these objectives in a computationally efficient manner suitable for real-time implementation is not straightforward. In this paper, we introduce a motion planning solution for enhanced target localization, leveraging Bernstein polynomial basis functions to approximate the probability distribution of the target's trajectory. This allows us to derive estimation performance criteria which are used by the motion planner to enhance the estimator efficacy. To conclude, we present simulation results that validate the effectiveness of the suggested algorithm.

On-line Motion Planning Using Bernstein Polynomials for Enhanced Target Localization in Autonomous Vehicles

TL;DR

The paper tackles online motion planning for target localization by a single autonomous vehicle under motion and safety constraints. It introduces a Bernstein-polynomial framework to represent both the vehicle trajectory and the target's probability distribution, embedding estimation performance via the determinant of the Fisher Information Matrix into a multi-objective NLP. Key contributions include a Bernstein approximation of the OCP with degree elevation, de Casteljau-based evaluation, and Bernstein-estimated PDF, with simulations showing that maximizing information yields faster and more accurate localization. The approach enables real-time, single-vehicle target localization across diverse sensing models and environments.

Abstract

The use of autonomous vehicles for target localization in modern applications has emphasized their superior efficiency, improved safety, and cost advantages over human-operated methods. For localization tasks, autonomous vehicles can be used to increase efficiency and ensure that the target is localized as quickly and precisely as possible. However, devising a motion planning scheme to achieve these objectives in a computationally efficient manner suitable for real-time implementation is not straightforward. In this paper, we introduce a motion planning solution for enhanced target localization, leveraging Bernstein polynomial basis functions to approximate the probability distribution of the target's trajectory. This allows us to derive estimation performance criteria which are used by the motion planner to enhance the estimator efficacy. To conclude, we present simulation results that validate the effectiveness of the suggested algorithm.
Paper Structure (8 sections, 24 equations, 3 figures, 1 table)

This paper contains 8 sections, 24 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Bernstein Approximation of Problem \ref{['prob:problemOCP']}
  4. Inequality constraints
  5. Boundary conditions
  6. Cost function
  7. Implementation and numerical results
  8. Conclusions

Figures (3)

  • Figure 1: Path traveled by the vehicle during the mission.
  • Figure 2: Estimation error over time.
  • Figure 3: Cumulative density function (top row) for $x$ and $y$ coordinates, respectively, and probability density function (bottom row) for $x$ and $y$ coordinates, respectively. The true position of the target is represented by the red vertical line.

Theorems & Definitions (2)

  • Remark 1
  • Remark 2