We present an approach to generate path-constrained synchronous motion for the coupled ensemble of robots. In this article, we refer to serial-link manipulators and mobile bases as robots. We assume that the relative motion constraints among the objects in the environment are given. We represent the motion constraints as path constraints and pose the problem of path-constrained synchronous trajectory generation as a non-linear optimization problem. Our approach generates configuration space trajectories for the robots to manipulate the objects such that the given motion constraints among the objects are satisfied. We present a method that formulates the problem as a discrete parameter optimization problem and solves it using successive constraint refinement techniques. The method adaptively selects the parametric representation of the configuration variables for a given scenario. It also generates an approximate solution as the starting point for the successive constraint refinement stages to reduce the computation time. We discuss in detail why successive constraint refinement strategies are useful for solving this class of problems. We demonstrate the effectiveness of the proposed method on challenging test cases in simulation and physical environments with high-degree-of-freedom robotic systems.

我们提出一种方法来为机器人的耦合集合生成路径受限的同步运动。在本文中，我们将串行链接操纵器和移动基座称为机器人。我们假设给出了环境中对象之间的相对运动约束。我们将运动约束表示为路径约束，并将路径约束的同步轨迹生成问题提出为非线性优化问题。我们的方法生成了用于机器人操纵对象的配置空间轨迹，从而满足了对象之间给定的运动约束。我们提出了一种将问题表述为离散参数优化问题并使用连续约束细化技术解决的方法。该方法针对给定场景自适应地选择配置变量的参数表示。它还会生成一个近似解作为连续约束细化阶段的起点，以减少计算时间。我们将详细讨论为什么连续约束细化策略对于解决此类问题很有用。我们演示了该方法在具有高自由度机器人系统的模拟和物理环境中挑战性测试用例中的有效性。