Planejamento de trajetórias robóticas utilizando B-splines

Abstract

Robot trajectory planning is the specification of the path the terminal element of the robot should move to accomplish a certain task. The trajectory planning can be done in the task domain or in the joints domain. For any domains that the trajectories are planned, it should be defined by a curve fitting function, such as approximation or interpolation of the points that define them. Many studies of curve fitting have been accomplish, in order to obtain smoother curves, so that the reference curve promoting the movement of the robot as smoothest as possible. The use of smooth curves in robotic avoid vibration of the robot along the path, wear of actuators and tracking error. For a trajectory be smooth, it must have at least position, velocity and acceleration continuity. Curves like polynomial, piecewise Hermite and splines are often used in trajectories of multi-axes machines. For the trajectories multipoint spline curve is commonly used, but if a point of this curve is changed, the entire profile of the curve is changed. To avoid this problem, some authors have been used B-spline, because it has local control, i.e., with the change of a control point, the curve changes only in a given region according to their continuity degree. Moreover, this type of curve has predictable behavior because it will always be contained within the polygon formed by its control points. This characteristic curve is called the convex hull property. In this master thesis is done the study of curves for robotic trajectory planning with concerning with B-spline and NURBS due to its great flexibility. Thus, from the curves study, was analyzed the type of curve used by industrial robot Motoman HP6. With the kinematic model of the robot Motoman HP6, it was proposed a trajectory planning using B-spline, since due to the convex hull property, simulations show that the trajectory in the joints domain has predictable behavior.