A Path Planning Algorithm for a Dynamic Environment Based on Proper Generalized Decomposition

Abstract

A necessity in the design of a path planning algorithm is to account for the environment. If the movement of the mobile robot is through a dynamic environment, the algorithm needs to include the main constraint: real-time collision avoidance. This kind of problem has been studied by different researchers suggesting different techniques to solve the problem of how to design a trajectory of a mobile robot avoiding collisions with dynamic obstacles. One of these algorithms is the artificial potential field (APF), proposed by O. Khatib in 1986, where a set of an artificial potential field is generated to attract the mobile robot to the goal and to repel the obstacles. This is one of the best options to obtain the trajectory of a mobile robot in real-time (RT). However, the main disadvantage is the presence of deadlocks. The mobile robot can be trapped in one of the local minima. In 1988, J.F. Canny suggested an alternative solution using harmonic functions satisfying the Laplace partial differential equation. When this article appeared, it was nearly impossible to apply this algorithm to RT applications. Years later a novel technique called proper generalized decomposition (PGD) appeared to solve partial differential equations, including parameters, the main appeal being that the solution is obtained once in life, including all the possible parameters. Our previous work, published in 2018, was the first approach to study the possibility of applying the PGD to designing a path planning alternative to the algorithms that nowadays exist. The target of this work is to improve our first approach while including dynamic obstacles as extra parameters.

Real-Time Path Planning Based on Harmonic Functions under a Proper Generalized Decomposition-Based Framework

“…In this sense, the immediate future work is related to the inclusion of mobile obstacles in the environment. There are various possibilities to take dynamic obstacles into account, such as the one studied in [39], where the disturbance in conductivity is used to model the presence of a moving obstacle, and the location of that conductivity disturbance is included as an additional parameter in the PGD formulation. Other future works imply the consideration of kinematic models for non-holonomic robots in the PGD framework and its use in solving the motion planning problem for unmanned aerial vehicles.…”

Identification of Differential Drive Robot Dynamic Model Parameters

“…AGV robots are a good solution for plants that are characterized by low variability of the production process and not very large distances between logistic destinations. In the case of frequent changes in the production process, dynamically changing environment in the plant (e.g., moving workers) [ 7 ], disturbances [ 8 , 9 ] and obstacles [ 10 ], a safe and flexible control system is required to allow for environmental changes [ 11 , 12 , 13 ] or reprogramming of the carts for other tasks. Searching for the most appropriate path planning algorithm according to user requirements can be challenging given the large number of examples existing in the literature [ 14 , 15 , 16 , 17 , 18 , 19 ].…”

Using Particle Swarm Optimization as Pathfinding Strategy in a Space with Obstacles

“…One of them uses an optimization process. However, traditional optimization techniques create local minima, and the robot may not reach its goal even if a solution exists [5]. Over the last few years, several heuristic algorithms have been introduced into path planning [6], including PSO.…”