Abstract
This paper presents a real-time global path planning method for mobile robots using harmonic functions, such as the Poisson equation, based on the Proper Generalized Decomposition (PGD) of these functions. The main property of the proposed technique is that the computational cost is negligible in real-time, even if the robot is disturbed or the goal is changed. The main idea of the method is the off-line generation, for a given environment, of the whole set of paths from any start and goal configurations of a mobile robot, namely the computational vademecum, derived from a harmonic potential field in order to use it on-line for decision-making purposes. Up until now, the resolution of the Laplace or Poisson equations has been based on traditional numerical techniques unfeasible for real-time calculation. This drawback has prevented the extensive use of harmonic functions in autonomous navigation, despite their powerful properties. The numerical technique that reverses this situation is the Proper Generalized Decomposition. To demonstrate and validate the properties of the PGD-vademecum in a potential-guided path planning framework, both real and simulated implementations have been developed. Simulated scenarios, such as an L-Shaped corridor and a benchmark bug trap, are used, and a real navigation of a LEGO®MINDSTORMS robot running in static environments with variable start and goal configurations is shown. This device has been selected due to its computational and memory-restricted capabilities, and it is a good example of how its properties could help the development of social robots.
Highlights
A fundamental robotic task is to plan collision-free motions among a set of static and known obstacles from a start to a goal position
The Proper Generalized Decomposition (PGD)-vademecum is generated considering that the solution of the potential field u solving (4) and (5) can be constructed as a finite sum of terms, each one consisting of the product of three functions: a function R of the environment X, a function W of the start configuration S and a function K of the target or goal configuration T: un−1 ( X, S, T ) =
In our previous work [24], the PGD was first introduced as an approach capable of using potential fields methods based on harmonic functions for real-time navigation
Summary
A fundamental robotic task is to plan collision-free motions among a set of static and known obstacles from a start to a goal position. Harmonic-based navigation allows dealing with errors in the model and in the mobile robot position, i.e., with uncertainty Despite their attractive properties, path planning based on harmonic functions has not been widely adopted because these functions cannot be computed in closed form and discrete approximations imply such a computational burden that has prevented their extensive use, as indicated in [15]. To demonstrate the capabilities of the proposed approach, a harmonic potential field based on the flow theory is used in simulated complex environments as well as in RT navigation experiments with a LEGO® MINDSTORMS robot in environments with static obstacles and variable start and goal robot configurations.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
