Planning with Discrete Harmonic Potential Fields

In this work a discrete counterpart to the continuous harmonic potential field approach is suggested. The extension to the discrete case makes use of the strong relation HPF-based planning has to connectionist artificial intelligence (AI). Connectionist AI systems are networks of simple, interconnected processors running in parallel within the confines of the environment in which the planning action is to be synthesized. It is not hard to see that such a paradigm naturally lends itself to planning on weighted graphs where the processors may be seen as the vertices of the graph and the relations among them as its edges. Electrical networks are an effective realization of connectionist AI. The utility of the discrete HPF (DHPF) approach is demonstrated in three ways. First, the capability of the DHPF approach to generate new, abstract, planning techniques is demonstrated by constructing a novel, efficient, optimal, discrete planning method called the M* algorithm. Also, its ability to augment the capabilities of existing planners is demonstrated by suggesting a generic solution to the lower bound problem faced by the A* algorithm. The DHPF approach is shown to be useful in solving specific planning problems in communication. It is demonstrated that the discrete HPF paradigm can support routing on-the-fly while the network is still in a transient state. It is shown by simulation that if a path to the target always exist and the switching delays in the routers are negligible, a packet will reach its destination despite the changes in the network which may simultaneously take place while the packet is being routed

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

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

Investigation of local minima in autonomous potential field agents/vehicles in pure dynamic environment

Autonomous vehicle navigation can be divided into two major areas of research: Collision avoidance and Track-Keeping. This study focuses on Collision avoidance which is one of the major issues that unmanned autonomous vehicles have to face. Collision avoidance may be further grouped into classical and soft computing based categories. Classical techniques are based on mathematical models and algorithms, while soft-computing techniques are based on Artificial Intelligence. In this study, we focus on the Classical techniques and more specifically in the Potential Field Methods. The potential field algorithms rapidly gained popularity due to their simplicity and elegance. In other words, Potential Field Methods are generic, computationally efficient and generate naturally smooth trajectories. On the other hand, PFM algorithms experience local minima. Nevertheless, local minima for PFM are extensively studied in different environments; they have never studied in a Pure Dynamic Environment (PDE). PDE is a new dynamic environment in which all its elements are guaranteed to be dynamic at their initial state. In this way we have managed to identify and define the causes of Potential Field Agent local minima and trajectory inefficiencies in a number of collision scenarios within PDE. To efficiently and accurately identify and define these causes of local minima and traj ectory inefficiencies, we have introduced the novel concept of the Monovular Autonomous Agent Correlation. Based on this concept we have identified and mathematically defined the Trajectory Equilibrium State (TES) for the first time. This state is responsible for local minima and trajectory inefficiencies of Monovular Autonomous Agents in PDE. Because of TES identification and definition we have designed a lUle based mathematical algorithm that efficiently navigates the Autonomous Agents out of local minima and trajectory inefficiencies in PDE in a number of generic collision scenarios. The algorithm's performance is tested in a number of simulated water based collision scenarios

Sampling-Based Motion Planning: A Comparative Review

Sampling-based motion planning is one of the fundamental paradigms to generate robot motions, and a cornerstone of robotics research. This comparative review provides an up-to-date guideline and reference manual for the use of sampling-based motion planning algorithms. This includes a history of motion planning, an overview about the most successful planners, and a discussion on their properties. It is also shown how planners can handle special cases and how extensions of motion planning can be accommodated. To put sampling-based motion planning into a larger context, a discussion of alternative motion generation frameworks is presented which highlights their respective differences to sampling-based motion planning. Finally, a set of sampling-based motion planners are compared on 24 challenging planning problems. This evaluation gives insights into which planners perform well in which situations and where future research would be required. This comparative review thereby provides not only a useful reference manual for researchers in the field, but also a guideline for practitioners to make informed algorithmic decisions.Comment: 25 pages, 7 figures, Accepted for Volume 7 (2024) of the Annual Review of Control, Robotics, and Autonomous System