We describe a novel 3D path following control framework for articulated robots in applications where constant speed travel along a path is desirable, such as robotic surface finishing tasks. Given the desired robot configuration sequence with a list of waypoints along a path, a trajectory optimization scheme based on direct collocation is proposed to determine the Cartesian path and the maximum constant translation speed that are dynamically feasible. Employing the Hermite–Simpson collocation method, a Cartesian path is developed that not only preserves the characteristics of the original motion sequence but also satisfies the physical requirements of the robot kinematics and dynamics. Since joint velocity control is quite common in many industrial robots, we consider a 3D kinematic control in the robot tool frame with control inputs as rate of change of orientation. The objective for the translation motion is to achieve constant speed along the path tangent direction, and that of the orientation control is to orient the robot properly based on the path provided by a converging path planner. We describe the optimization procedure employed with the direct collocation method to obtain the desired Cartesian path, an arc-length based re-parametrization of the desired path, and a path planner that provides a converging path to the desired path. To perform the surface finishing operation, we further present the joint space control law that is converted from the synthesis of the proposed path following and impedance force control in the tool frame. To verify and evaluate the performance of the proposed framework, we have conducted extensive experiments with a six degrees-of-freedom (DOF) industrial robot for several paths that can be employed for surface finishing of a variety of industrial parts.

我们描述了一种适用于铰接式机器人的新颖3D路径控制框架，该控制框架适用于需要沿路径以恒定速度行进的应用，例如机器人表面精加工任务。给定所需的机器人配置序列以及沿路径的一系列路点，提出了一种基于直接配置的轨迹优化方案，以确定动态可行的笛卡尔路径和最大恒定平移速度。利用Hermite-Simpson搭配方法，开发了笛卡尔路径，该路径不仅保留了原始运动序列的特征，而且还满足了机器人运动学和动力学的物理要求。由于关节速度控制在许多工业机器人中非常普遍，我们将机器人工具框架中的3D运动控制与方向输入的变化率作为控制输入。平移运动的目标是沿路径切线方向实现恒定速度，而方向控制的目标是基于会聚路径规划器提供的路径正确地对机器人进行定向。我们描述了与直接配置方法一起使用的优化过程，以获取所需的笛卡尔路径，基于弧长的所需路径的重新参数化，以及提供会聚路径至所需路径的路径规划器。为了执行表面精加工操作，我们进一步提出了关节空间控制定律，该定律是从拟议的路径跟踪和工具框架中的阻抗力控制的综合转换而来的。