In this paper, we describe an algorithm for predicting future positions and orientation of a moving object in a time-varying environment using an autoregressive model (ARM). No constraint is placed on the obstacles motion. The model addresses prediction of translational and rotational motions. Rotational motion is represented using quaternions rather than Euler representation to improve the algorithm performance and accuracy of the prediction results. Compared to other similar systems, the proposed algorithm has an adaptive capability, which enables it to predict over multiple time-steps rather than fixed ones as reported in other works. Such algorithm can be used in a variety of applications. An important one is its application in the framework of designing reliable navigational systems for autonomous mobile robots and more particularly in building effective trajectory planners. Simulation results show how significantly this model could reduce computational cost.

This paper presents a new algorithm to the motion planning problem for a mobile robot in a local environment. The algorithm uses the step-by-step approach to move the robot along the line that joins the starting point and the goal point. When an obstacle is met the algorithm assigns a value to each one of the eight surrounding points that surround the current point then the robot moves to the point that has the minimum value. Each obstacle point is assigned a relatively large value, while the value assigned to a non-obstacle point is the algebraic sum of the horizontal and the vertical distances from the goal point. The proposed algorithm completely eliminates the local minima problem, which is exhibited in most artificial-potential based methods, and most important it eliminates the "flat-regions" problem. The proposed algorithm is superior to other algorithms because of its low-computational cost besides simplicity. It also outperforms the blind-follow based algorithms. Simulation results demonstrates the validity and the potential of the proposed algorithm.

This paper presents a new formulation of the artificial potential approach to the motion planning problem for a mobile robot in a global environment. To model the potential (magnetic) field by Maxwell's Equations that completely eliminate the local minima problem, which is exhibited in most artificial potential methods, such as Harmonic functions based methods. However, the proposed model is superior to the Harmonic one because it is easily extendable to 3D, the time dimension is modeled by default which means it is a suitable model for time-varying environments, computations are less and hence faster, and most important it eliminates the "flat-regions" problem. In this work, electrical currents are assumed to be floating in a cluttered environment with obstacles. The obstacles are assigned zero conductivity whereas the goal point is assigned the highest electrical conductivity. The magnetic field induced by the electric currents is used to find a free path between the start and goal points. Simulation results reflects the validity and the potential of the proposed model.

An approach to generating acceleration-based optimal smooth piecewise trajectories is proposed. Given two configurations (position and orientation) in 3D, we search for the minimal energy trajectory that minimizes the integral of the squared acceleration, opposed to curvature, which is widely investigated. The variation in both components of acceleration controls the smoothness of generated trajectories. Our objective is to search for the trajectory along which a free moving robot is able to accelerate (decelerate) to a safe speed in an optimal way. A numerical iterative procedure is devised for computing the optimal piecewise trajectory as a solution of a constrained boundary value problem.

A novel approach to generating optimal smooth piecewise trajectories based on a new energy measure is proposed. Given the configurations (position and direction) of two points in the plane, we search for the minimal energy trajectory that minimizes the integral of the squared acceleration opposed to curvature, which has been the predominant energy measure studied in the literature. The smoothness of the optimal trajectory depends on how the tangential and normal components of acceleration vary over an interval of time. A numerical iterative procedure is devised for computing the optimal piecewise trajectory as a solution of a constrained boundary value problem. The resulting trajectories are not only smooth but also safe with optimal velocity (acceleration) profiles and therefore suitable for robot motion planning applications. The feasibility of the proposed approach is illustrated by several simulation examples. Besides motion planning, the resulting trajectories may be useful in computer graphics and geometric design.