Speed Computation for Industrial Robot Motion by Accurate Positioning

In this paper we define a new method for speed (velocity) computation, named mixt profile. The mixt profile of speed variation assures an accurate positioning at the end of motion (movement), in a well determinate time lapse. The method is linked with computation of location (position) matrix, about an industrial robot. Mixt profile of speed may be applied about motion on linear or circular trajectories. The paper continues the explanation from [6] regarding this method

Continuous collision detection for ellipsoids

We present an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids. We start with a highly optimized implementation of interference testing between two stationary ellipsoids based on an algebraic condition described in terms of the signs of roots of the characteristic equation of two ellipsoids. Then we derive a time-dependent characteristic equation for two moving ellipsoids, which enables us to develop a real-time algorithm for computing the time intervals in which two moving ellipsoids collide. The effectiveness of our approach is demonstrated with several practical examples. © 2006 IEEE.published_or_final_versio

Error bounded approximate reparametrization of NURBS curves

Journal ArticleThis paper reports research on solutions to the following reparametrization problem: approximate c(r(t)) by a NURBS where c is a NURBS curve and r may, or may not, be a NURBS function. There are many practical applications of this problem including establishing and exploring correspondence in geometry, creating related speed profiles along motion curves for animation, specifying speeds along tool paths, and identifying geometrically equivalent, or nearly equivalent, curve mappings. A framework for the approximation problem is described using two related algorithmic schemes. One constrains the shape of the approximation to be identical to the original curve c. The other relaxes this constraint. New algorithms for important cases of curve reparametrization are developed from within this framework. They produce results with bounded error and address approximate arc length parametrizations of curves, approximate inverses of NURBS functions, and reparametrizations that establish user specified tolerances as bounds on the Frechet distance between parametric curves

Design of a cognitive neural predictive controller for mobile robot

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel UniversityIn this thesis, a cognitive neural predictive controller system has been designed to guide a nonholonomic wheeled mobile robot during continuous and non-continuous trajectory tracking and to navigate through static obstacles with collision-free and minimum tracking error. The structure of the controller consists of two layers; the first layer is a neural network system that controls the mobile robot actuators in order to track a desired path. The second layer of the controller is cognitive layer that collects information from the environment and plans the optimal path. In addition to this, it detects if there is any obstacle in the path so it can be avoided by re-planning the trajectory using particle swarm optimisation (PSO) technique. Two neural networks models are used: the first model is modified Elman recurrent neural network model that describes the kinematic and dynamic model of the mobile robot and it is trained off-line and on-line stages to guarantee that the outputs of the model will accurately represent the actual outputs of the mobile robot system. The trained neural model acts as the position and orientation identifier. The second model is feedforward multi-layer perceptron neural network that describes a feedforward neural controller and it is trained off-line and its weights are adapted on-line to find the reference torques, which controls the steady-state outputs of the mobile robot system. The feedback neural controller is based on the posture neural identifier and quadratic performance index predictive optimisation algorithm for N step-ahead prediction in order to find the optimal torque action in the transient to stabilise the tracking error of the mobile robot system when the trajectory of the robot is drifted from the desired path during transient state. Three controller methodologies were developed: the first is the feedback neural controller; the second is the nonlinear PID neural feedback controller and the third is nonlinear inverse dynamic neural feedback controller, based on the back-stepping method and Lyapunov criterion. The main advantages of the presented approaches are to plan an optimal path for itself avoiding obstructions by using intelligent (PSO) technique as well as the analytically derived control law, which has significantly high computational accuracy with predictive optimisation technique to obtain the optimal torques control action and lead to minimum tracking error of the mobile robot for different types of trajectories. The proposed control algorithm has been applied to monitor a nonholonomic wheeled mobile robot, has demonstrated the capability of tracking different trajectories with continuous gradients (lemniscates and circular) or non-continuous gradients (square) with bounded external disturbances and static obstacles. Simulations results and experimental work showed the effectiveness of the proposed cognitive neural predictive control algorithm; this is demonstrated by the minimised tracking error to less than (1 cm) and obtained smoothness of the torque control signal less than maximum torque (0.236 N.m), especially when external disturbances are applied and navigating through static obstacles. Results show that the five steps-ahead prediction algorithm has better performance compared to one step-ahead for all the control methodologies because of a more complex control structure and taking into account future values of the desired one, not only the current value, as with one step-ahead method. The mean-square error method is used for each component of the state error vector to compare between each of the performance control methodologies in order to give better control results