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Fuzzy-Logic-based model predictive control: A paradigm integrating optimal and common-sense decision making

Filip Surma, Anahita Jamshidnejad

TL;DR

The paper tackles search-and-rescue in unknown environments by replacing Bayesian MPC with a fuzzy-logic-based model predictive control (FLMPC) that uses dynamic fuzzy maps for perception. It introduces a bi-level, parent–child FLMPC architecture to extend decision horizons and improve coordination among multiple robots. The core contributions are the FLMPC framework with three aggregation steps, the bi-level architecture, and two case studies showing significant reductions in computation and improvements in mission completion reliability. The approach offers a scalable, robust alternative for large-scale, uncertain USaR missions, with practical impact in autonomous multi-robot coordination and exploration efficiency.

Abstract

This paper introduces a novel concept, fuzzy-logic-based model predictive control (FLMPC), along with a multi-robot control approach for exploring unknown environments and locating targets. Traditional model predictive control (MPC) methods rely on Bayesian theory to represent environmental knowledge and optimize a stochastic cost function, often leading to high computational costs and lack of effectiveness in locating all the targets. Our approach instead leverages FLMPC and extends it to a bi-level parent-child architecture for enhanced coordination and extended decision making horizon. Extracting high-level information from probability distributions and local observations, FLMPC simplifies the optimization problem and significantly extends its operational horizon compared to other MPC methods. We conducted extensive simulations in unknown 2-dimensional environments with randomly placed obstacles and humans. We compared the performance and computation time of FLMPC against MPC with a stochastic cost function, then evaluated the impact of integrating the high-level parent FLMPC layer. The results indicate that our approaches significantly improve both performance and computation time, enhancing coordination of robots and reducing the impact of uncertainty in large-scale search and rescue environments.

Fuzzy-Logic-based model predictive control: A paradigm integrating optimal and common-sense decision making

TL;DR

The paper tackles search-and-rescue in unknown environments by replacing Bayesian MPC with a fuzzy-logic-based model predictive control (FLMPC) that uses dynamic fuzzy maps for perception. It introduces a bi-level, parent–child FLMPC architecture to extend decision horizons and improve coordination among multiple robots. The core contributions are the FLMPC framework with three aggregation steps, the bi-level architecture, and two case studies showing significant reductions in computation and improvements in mission completion reliability. The approach offers a scalable, robust alternative for large-scale, uncertain USaR missions, with practical impact in autonomous multi-robot coordination and exploration efficiency.

Abstract

This paper introduces a novel concept, fuzzy-logic-based model predictive control (FLMPC), along with a multi-robot control approach for exploring unknown environments and locating targets. Traditional model predictive control (MPC) methods rely on Bayesian theory to represent environmental knowledge and optimize a stochastic cost function, often leading to high computational costs and lack of effectiveness in locating all the targets. Our approach instead leverages FLMPC and extends it to a bi-level parent-child architecture for enhanced coordination and extended decision making horizon. Extracting high-level information from probability distributions and local observations, FLMPC simplifies the optimization problem and significantly extends its operational horizon compared to other MPC methods. We conducted extensive simulations in unknown 2-dimensional environments with randomly placed obstacles and humans. We compared the performance and computation time of FLMPC against MPC with a stochastic cost function, then evaluated the impact of integrating the high-level parent FLMPC layer. The results indicate that our approaches significantly improve both performance and computation time, enhancing coordination of robots and reducing the impact of uncertainty in large-scale search and rescue environments.

Paper Structure

This paper contains 36 sections, 16 equations, 8 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Solution proposed in this paper
  3. Main contribution and structure of the paper
  4. Related work
  5. Fuzzy decision making
  6. MPC in exploration of unknown environments via robots
  7. Proposed methods
  8. Problem statement
  9. Fuzzy-logic-based model predictive control (FLMPC)
  10. Aggregating the importance degrees for all fuzzy goals
  11. Aggregating the satisfaction degrees for all fuzzy constraints
  12. Overall aggregation for determining the solution of FLMPC
  13. Optimization problem of FLMPC
  14. FLMPC for exploring unknown environments
  15. Mapping unknown environments
  16. ...and 21 more sections

Figures (8)

  • Figure 1: Three fuzzy clusters, numbered 1 to 3, are illustrated in different colors: In this case there is a wall (shown in dark blue) that is identified, leading to the division of the first fuzzy cluster into three smaller fuzzy sub-clusters (shown in yellow). Each sub-cluster is represented by a letter A, B or C. Given that the sub-cluster C is the largest (i.e., it includes more environmental cells), it is considered as the fuzzy cluster 1 that should replace the original fuzzy cluster 1. Since the fuzzy sub-cluster B that is totally encountered by the wall is not connected to any other fuzzy (sub-)clusters, it cannot be included in any trajectories by the high-level FLMPC system. The fuzzy sub-cluster A is be merged with cluster 3 by the parent FLMPC system.
  • Figure 2: The control diagram is presented from the perspective of a single robot.
  • Figure 3: A randomly generated environment for the first case study: In this environment, white is used to represent empty spaces, black is used to represent the obstacles, green is used to represent humans, and blue is used to represent the robots.
  • Figure 4: Top left: Membership function for the passability of a cell, given the likelihood that the state of the cell is "obstacle". Top right: Membership function for human detection reward for a cell, given the likelihood that the state of the cell is "human". Bottom left: Membership function for exploration reward for a cell, given the uncertainty of the cell within $[0,1]$. Bottom right: Evolution of the uncertainty degree for a cell; uncertainty degree raises over time as long as the cell is not visited/observed.
  • Figure 5: Left: Membership function for "uncertainty" when the cell is observed, given the most recent value for the uncertainty degree and for the measurement consistency degree. Right: Membership function for "measurement consistency", given the detectability of the cell and the likelihood for a measurement.
  • ...and 3 more figures

Theorems & Definitions (6)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6