# Time Distance: A Novel Collision Prediction and Path Planning Method

## TL;DR

This paper introduces Time Distance, a fast path planning and collision prediction method in dynamic environments, utilizing space-time concepts to generate length optimal collision-free paths efficiently.

## Contribution

The paper presents the novel Time Distance (TD) algorithm and a collision prediction framework that leverage space-time space ideas for improved path planning in dynamic settings.

## Key findings

- The TD-based algorithm is fast and capable of generating length optimal paths.
- Simulation results show the method outperforms existing approaches in speed and optimality.
- The collision prediction framework accurately calculates collision times using TD functions.

## Abstract

In this paper, a new fast algorithm for path planning and a collision prediction framework for two dimensional dynamically changing environments are introduced. The method is called Time Distance (TD) and benefits from the space-time space idea. First, the TD concept is defined as the time interval that must be spent in order for an object to reach another object or a location. Next, TD functions are derived as a function of location, velocity and geometry of objects. To construct the configuration-time space, TD functions in conjunction with another function named "Z-Infinity" are exploited. Finally, an explicit formula for creating the length optimal collision free path is presented. Length optimization in this formula is achieved using a function named "Route Function" which minimizes a cost function. Performance of the path planning algorithm is evaluated in simulations. Comparisons indicate that the algorithm is fast enough and capable to generate length optimal paths as the most effective methods do. Finally, as another usage of the TD functions, a collision prediction framework is presented. This framework consists of an explicit function which is a function of TD functions and calculates the TD of the vehicle with respect to all objects of the environment.

---
Source: https://tomesphere.com/paper/1907.03244