This paper presents a novel algorithm for industrial robot trajectory planning based on the NURBS(Non-Uniform Rational B-Spline) curve and Slerp interpolation aiming at the problems that the trajectory of a six-axis industrial robot is not smooth enough in the operation process, the posture planning process is non-uniform, and the six-axis industrial robot starts and stops frequently. Firstly, aiming at the first problem, the trajectory planning algorithm based on the NURBS curve is presented to improve the smoothness of the trajectory curve. Combined with Slerp posture planning based on quaternion description, which realizes the uniform change of posture on the robot’s end-effector. Secondly, aiming at the second problem, the S-velocity planning algorithm is presented in the interpolation interval of the robot, which realizes the operation process of complex curves continuously, and improves the operation quality. Finally, this paper uses Bernoulli’s lemniscate as the incentive trajectory, and the contrast experiment of trajectory planning between two incentive profiles is designed, which are the NURBS curve and the five-order polynomial curve. The result of the experiment indicates that the planning algorithm proposed in this paper could effectively improve the smoothness of trajectory in a Cartesian workspace, decrease the impact and tremulous in a Cartesian workspace, and effectively improve the performance of the robot working process. The results drawn from this paper lay a certain foundation for the future high-precision control of industrial robots.

This paper presents a novel algorithm about the industrial robot contouring control based on the NURBS (non-uniform rational B-spline) curve. First, aiming at the error between the industrial robot’s actual trajectory and the desired trajectory, the contour error is proposed as the trajectory evaluation index, and the estimation algorithm of contour error based on the tangent approximation is proposed. Based on the tangent approximation algorithm, the estimation algorithm of contour error in the local task coordinate frame is proposed to realize the transformation from the Cartesian coordinate frame to the local task coordinate frame. Second, according to the configuration of the industrial robot, a modified cross-coupling control scheme based on the local task coordinate frame is designed. Finally, the Bernoulli’s lemniscate curves are constructed by NURBS curve and five-order polynomial curve, respectively, and they are symmetrical. The contrast experiment is designed using the two types of constructed Bernoulli’s lemniscate curves as the incentive trajectory. Through the analysis and comparison between the obtained uniaxial tracking error and the contour error curve of the two incentive trajectories, it is concluded that the incentive trajectory constructed by the NURBS curve has better contour control performance than that constructed by the five-order polynomial curve. The results drawn from this paper lay a certain foundation for the future high-precision contouring control of industrial robots.