Abstract:  In order to increase the speeds of the robot arms tracking the target trajectory, the target trajectory of the robots was re-planned. By introducing path parameters, constraints such as joint velocity and force/moment were transformed into constraints on trajectory parameters in the trajectory planning algorithm. The maximum velocity curves of path parameters under joint velocity and force/moment constraints were obtained respectively. The maximum velocity curves with multiple constraints were obtained by calculating the intersection of the above maximum velocity curves. In order to improve the computational efficiency of the algorithm, the fuzzy inference method was used to discretize the target trajectory to reduce the optimization scales, and the maximum velocity curves of the joint force/torque constraint were replaced by the velocity curves of the zero value acceleration curves multiplied by the proportional coefficient. The planned trajectory was modified through the speed feature point algorithm and the modification-target algorithm to ensure that the modified target trajectory meets the constraints of joint speed and force/torque, and the velocity curve is smooth. The trajectory planning experimental results shows that the trajectory planning algorithm have better planning performance for target trajectories of different complexity, and may obtain continuous and smooth time approximate optimal trajectories.

Key words: robot, kinematics model, dynamics model, time approximate optimal, trajectory planning

摘要： 为了提高机械臂跟踪目标轨迹的运动速度，对其目标轨迹进行二次规划。该轨迹规划算法通过引入路径参数s，将关节速度、力/力矩等约束转化为关于路径参数的约束，分别求取关节速度与力/力矩约束限制下路径参数s的最大速度曲线，对最大速度曲线求交集，获得多重约束最大速度曲线。采用模糊推理方法对目标轨迹进行离散化处理，减小优化规模；以0值加速度曲线乘以比例系数Kv替代关节力/力矩约束的最大速度曲线，提高算法的计算效率；通过速度特征点算法与修型射靶算法对规划得到的轨迹进行修形，确保修形后的目标轨迹满足关节速度、力/力矩的约束，并且速度曲线光滑。实验表明，该轨迹规划算法对不同复杂程度的目标轨迹都有着较好的规划性能，能够得到连续平滑的时间近似最优轨迹。

关键词: 机器人, 运动学模型, 动力学模型, 时间近似最优, 轨迹规划