A rational B-Spline curves in robot collision - free movement planning

In this paper there is described the using of 2D robot workspace analysis method with smoothing process by using B-Spline curves [7]. The robot workspace analysis is necessary to generate the collision-free movement paths. This paper is connected with a project, which will be ended with fully functional added application in robot off-line programming. In the last part of this project the authors created the motion planner based on grading function and Markov chains. This planner allows determining the collision-free trajectory of robot bunch. Determining the collision-free trajectory generates a lot of step functions – all movements were possible in only one direction (parallel to Cartesian axes) [1,7]. The worked out planner choose the best path – by shortest movement length or shortest movement time criterion. Achieved path is optimised and smooth by using NURBS and B-Spline curves [2,4,5], which is the main goal of this paper. Smoothing and time-function making is very important, because it allows getting the speed and acceleration data, which are necessary in robot controlling. B-Spline curves fulfil continuous first and second derivate condition. Another advantage of using B-Spline is a possibility to enlarge the movement quality by using the minimal acceleration criteria. This allows growing the steadiness of movement.