Research On Orientation Trajectory Planning Based On Quaternion Spline Curve

In recent years, industrial robot technology is having much rapid development. Motion control is one of the key technologies of industrial robots, and the trajectory planning of which impacts on its accuracy and efficiency directly. Trajectory planning is generally divided into position trajectory planning and orientation trajectory planning. There are several representing methods of orientation, such as Euler angles, rotation matrix, and so on. Unfortunately, the interpolation difficult or singularity may occur when using those methods. However, quaternion has no similar issues. Thus, this thesis uses quaternion spline curve as orientation interpolation curve for orientation trajectory planning.For the sake of orientation continuous trajectory planning with multi-teaching-points, quaternion spline curve as the orientation interpolation curve is researched. The control points in the head and the tail are increased through spherical linear interpolation so that the head and the tail of quaternion spline curve coincide with the first and the end teaching point, and every teaching point coincides with the quaternions corresponding to node vector parameter. And a general type of smooth transition curve between multi-interpolation-curves is obtained based on given boundary conditions of quaternions, first and second derivatives.Further, the orientation trajectory planning algorithms based on quaternion spline curve is researched, mainly including forward and backward curve fitting, transformation from quaternion to orientation space. In order to obtain orientation angular displacement, the relationship between quaternion along with its derivative and angular velocity is researched, and the angular displacement is received through the composite cotes formulas for numerical integration. In order to get the vector-velocity and vector-acceleration, the knot u about angular displacement θ is reversed out by third-order Hermit interpolation firstly, the first and second derivative of knot u about time is obtained by the mean of middle finite difference method then, so the velocity and acceleration obtained by S-type velocity planning can be vectorized utilizing the relationship between quaternion derivative and angular velocity.By establishing the model of robot, simulation is worked in the MATLAB software. The simulation verified the feasibility and effectiveness of the algorithms proposed in this paper.