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Towards Local Minima-free Robotic Navigation: Model Predictive Path Integral Control via Repulsive Potential Augmentation

Takahiro Fuke, Masafumi Endo, Kohei Honda, Genya Ishigami

TL;DR

Results show that the proposed motion planning method guarantees the avoidance of local minima and outperforms existing methods in terms of global optimality without decreasing computational efficiency.

Abstract

Model-based control is a crucial component of robotic navigation. However, it often struggles with entrapment in local minima due to its inherent nature as a finite, myopic optimization procedure. Previous studies have addressed this issue but sacrificed either solution quality due to their reactive nature or computational efficiency in generating explicit paths for proactive guidance. To this end, we propose a motion planning method that proactively avoids local minima without any guidance from global paths. The key idea is repulsive potential augmentation, integrating high-level directional information into the Model Predictive Path Integral control as a single repulsive term through an artificial potential field. We evaluate our method through theoretical analysis and simulations in environments with obstacles that induce local minima. Results show that our method guarantees the avoidance of local minima and outperforms existing methods in terms of global optimality without decreasing computational efficiency.

Towards Local Minima-free Robotic Navigation: Model Predictive Path Integral Control via Repulsive Potential Augmentation

TL;DR

Results show that the proposed motion planning method guarantees the avoidance of local minima and outperforms existing methods in terms of global optimality without decreasing computational efficiency.

Abstract

Model-based control is a crucial component of robotic navigation. However, it often struggles with entrapment in local minima due to its inherent nature as a finite, myopic optimization procedure. Previous studies have addressed this issue but sacrificed either solution quality due to their reactive nature or computational efficiency in generating explicit paths for proactive guidance. To this end, we propose a motion planning method that proactively avoids local minima without any guidance from global paths. The key idea is repulsive potential augmentation, integrating high-level directional information into the Model Predictive Path Integral control as a single repulsive term through an artificial potential field. We evaluate our method through theoretical analysis and simulations in environments with obstacles that induce local minima. Results show that our method guarantees the avoidance of local minima and outperforms existing methods in terms of global optimality without decreasing computational efficiency.

Paper Structure

This paper contains 18 sections, 18 equations, 4 figures, 1 table.

Figures (4)

  • Figure 1: Illustrative comparison of motion planning methods, motivated by the local minima problem around a large obstacle. Methods vary in solution optimality and computational efficiency, as detailed in subcaptions (a)-(c).
  • Figure 2: Coordinate system setting for theoretical analysis. The position indicated as local minimum and the associated regions illustrated are based on the conventional squared Euclidean distance-based cost.
  • Figure 3: Three obstacle configurations are tested across 24 initial states. Initial Heading Angles [rad]: {$\frac{\pi}{4}$, $\frac{\pi}{2}$, $\frac{5}{4}\pi$, $\frac{3}{2}\pi$}; Initial positions [m]: {(10, 1), (1, 1), (19, 1), (10, 8.5), (1, 8.5), (19, 8.5)}
  • Figure 4: Comparison of executed trajectories with Long-wid obstacle. (a) Std-MPPI: Fails to reach the goal due to local minima. (b) A*-MPPI: Reaches the goal with a reference path. (c) RPA-MPPI (ours): Reaches the goal without a reference path, adjusting speed and trajectory near obstacles.

Theorems & Definitions (3)

  • proof
  • proof
  • proof