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

Optimal control subsumes harmonic control

We consider trajectory planning within the frameworks of optimal control and harmonic control. We present a formal evidence, in continuous domain and in a standard discretization, that harmonic control is the limit case of a some optimal control problem in which we make the noise level tend to infinity. In other words we show that optimal control subsumes harmonic control. We discuss properties of both paradigms and present simulations that illustrate this relationship

A survey of formation control and motion planning of multiple unmanned vehicles

The increasing deployment of multiple unmanned vehicles systems has generated large research interest in recent decades. This paper therefore provides a detailed survey to review a range of techniques related to the operation of multi-vehicle systems in different environmental domains, including land based, aerospace and marine with the specific focuses placed on formation control and cooperative motion planning. Differing from other related papers, this paper pays a special attention to the collision avoidance problem and specifically discusses and reviews those methods that adopt flexible formation shape to achieve collision avoidance for multi-vehicle systems. In the conclusions, some open research areas with suggested technologies have been proposed to facilitate the future research development

On-Orbit Manoeuvring Using Superquadric Potential Fields

On-orbit manoeuvring represents an essential process in many space missions such as orbital assembly, servicing and reconfiguration. A new methodology, based on the potential field method along with superquadric repulsive potentials, is discussed in this thesis. The methodology allows motion in a cluttered environment by combining translation and rotation in order to avoid collisions. This combination reduces the manoeuvring cost and duration, while allowing collision avoidance through combinations of rotation and translation. Different attractive potential fields are discussed: parabolic, conic, and a new hyperbolic potential. The superquadric model is used to represent the repulsive potential with several enhancements. These enhancements are: accuracy of separation distance estimation, modifying the model to be suitable for moving obstacles, and adding the effect of obstacle rotation through quaternions. Adding dynamic parameters such as object translational velocity and angular velocity to the potential field can lead to unbounded actuator control force. This problem is overcome in this thesis through combining parabolic and conic functions to form an attractive potential or through using a hyperbolic function. The global stability and convergence of the solution is guaranteed through the appropriate choice of the control laws based on Lyapunov's theorem. Several on-orbit manoeuvring problems are then conducted such as on-orbit assembly using impulsive and continuous strategies, structure disassembly and reconfiguration and free-flyer manoeuvring near a space station. Such examples demonstrate the accuracy and robustness of the method for on-orbit motion planning