Planning collision-free and smooth joint motion is crucial in robotic applications, such as welding, milling, and laser cutting. Kinematic redundancy exists when a six-axis industrial robot performs five-dimensional tasks, and there are infinite joint configurations for a six-axis industrial robot to realize a cutter location data of the tool path. The robot joint motion can be optimized by taking advantage of the kinematic redundancy, and the collision-free joint motion with minimum joint movement is determined as the optimal. However, most existing redundancy optimization methods do not fully exploit the redundancy of the six-axis industrial robots when they conduct five-dimensional tasks. In this paper, we present an optimization method to solve the problem of inverse kinematics for a six-axis industrial robot to synthesize the joint motion that follows a given tool path, while achieving smoothness and collision-free manipulation. B-spline is applied for the joint configuration interpolation, and the sum of the squares of the first, second, and third derivatives of the B-spline curves are adopted as the smoothness indicators. Besides, the oriented bounding boxes are adopted to simplify the shape of the robot joints, robot links, spindle unit, and fixtures to facilitate collision detections. Dijkstra's shortest path technique and Differential Evolution algorithm are combined to find the optimal joint motion efficiently and avoid getting into a local optimal solution. The proposed algorithm is validated by simulations on two six-axis industrial robots conducting five-axis flank milling tasks respectively.

在机器人应用（例如焊接，铣削和激光切割）中，规划无碰撞且平稳的关节运动至关重要。当六轴工业机器人执行五维任务时，存在运动冗余，并且六轴工业机器人具有无限的关节构造，以实现刀具路径的刀具位置数据。可以利用运动学冗余性来优化机器人的关节运动，并且将具有最小关节运动的无碰撞关节运动确定为最佳。但是，大多数现有的冗余优化方法在执行五维任务时并未充分利用六轴工业机器人的冗余。在本文中，我们提出一种优化方法，以解决六轴工业机器人的逆运动学问题，以合成遵循给定工具路径的关节运动，同时实现平滑性和无碰撞的操纵。将B样条曲线应用于关节构造插值，并采用B样条曲线的一阶，二阶和三阶导数的平方和作为平滑度指标。此外，采用定向包围盒来简化机器人关节，机器人连杆，主轴单元和固定装置的形状，以便于碰撞检测。Dijkstra的最短路径技术和差分进化算法相结合，可以有效地找到最佳的关节运动，并且避免陷入局部最优解。