# Study of dynamical system based obstacle avoidance via manipulating orthogonal coordinates

## TL;DR

This paper introduces a novel obstacle avoidance method using orthogonal coordinate manipulation within dynamical systems, improving motion reasoning and solving local minima issues in high-dimensional spaces.

## Contribution

It develops a new modulation matrix based on orthogonal coordinates and a rotating matrix approach for better obstacle avoidance in complex environments.

## Key findings

- Effective obstacle avoidance demonstrated in 3D and higher dimensions.
- Resolves local minima problems in dynamical system-based navigation.
- Applicable to patrolling around convex shapes.

## Abstract

In this paper, we consider the general problem of obstacle avoidance based on dynamical system. The modulation matrix is developed by introducing orthogonal coordinates, which makes the modulation matrix more reasonable. The new trajectory's direction can be represented by the linear combination of orthogonal coordinates. A orthogonal coordinates manipulating approach is proposed by introducing rotating matrix to solve the local minimal problem and provide more reasonable motions in 3-D or higher dimension space. The proposed method also provide a solution for patrolling around a convex shape. Experimental results on several designed dynamical systems demonstrate the effectiveness of the proposed approach.

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Source: https://tomesphere.com/paper/1902.05343