Obstacle avoidance &motion planning by stochastic processes, spatial description, sensor integration and trajectory generation in the domain of embedded systems, mechatronics, artificial intelligence, robotics and machine learning

In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map contains the estimates of relationships among objects in the map, and their uncertainties, given all the available information. The procedures provide a general solution to the problem of estimating uncertain relative spatial relationships and trajectory description. The estimates are probabilistic in nature, an advance over the previous, very conservative, worst-case approaches to the problem. Finally, the procedures are developed in the context of state-estimation and filtering theory, which provides a solid basis for numerous extensions. Traditionally, the dynamic model, i.e., the equations of motion, of a robotic system is derived from Euler–Lagrange (EL) or Newton–Euler (NE) equations. The EL equations begin with a set of generally independent generalized coordinates, whereas the NE equations are based on the Cartesian coordinates. The NE equations consider various forces and moments on the free body diagram of each link of the robotic system at hand, and, hence, require the calculation of the constrained forces and moments that eventually do not participate in the motion of the coupled system. Hence, the principle of elimination of constraint forces has been proposed in the literature. One such methodology is based on the Decoupled Natural Orthogonal Complement (DeNOC) matrices, reported elsewhere. It is shown in this paper that one can also begin with the EL equations of motion based on the kinetic and potential energies of the system, and use the DeNOC matrices to obtain the independent equations of motion. The advantage of the proposed approach is that a computationally more efficient forward dynamics algorithm for the serial robots having slender rods is obtained, which is numerically stable. The typical six-degree-of-freedom PUMA robot is considered here to illustrate the advantages of the proposed algorithm. Moreover obstacle avoidance, motion planning and dynamic simulation comes in the trajectory generation part. Spatial description and trajectory generation work simultaneously for the proper functioning of the robot. Joint-space trajectory generation is in common usage in robotics to provide smooth, continuous motion from one set of n joint angles to another, for instance for moving between two distinct Cartesian poses for which the inverse pose solution has yielded two distinct sets of n joint angles. The joint-space trajectory generation occurs at runtime for all n joints independently but simultaneously.