We propose coordinating guiding vector fields to achieve two tasks simultaneously with a team of robots: first, the guidance and navigation of multiple robots to possibly different paths or surfaces typically embedded in 2D or 3D; second, their motion coordination while tracking their prescribed paths or surfaces. The motion coordination is defined by desired parametric displacements between robots on the path or surface. Such a desired displacement is achieved by controlling the virtual coordinates, which correspond to the path or surface's parameters, between guiding vector fields. Rigorous mathematical guarantees underpinned by dynamical systems theory and Lyapunov theory are provided for the effective distributed motion coordination and navigation of robots on paths or surfaces from all initial positions. As an example for practical robotic applications, we derive a control algorithm from the proposed coordinating guiding vector fields for a Dubins-car-like model with actuation saturation. Our proposed algorithm is distributed and scalable to an arbitrary number of robots. Furthermore, extensive illustrative simulations and fixed-wing aircraft outdoor experiments validate the effectiveness and robustness of our algorithm.
翻译:我们提议与一组机器人同时协调指导矢量场,以完成两项任务:第一,多机器人的指导和导航到通常嵌入于2D或3D的不同路径或表面;第二,在跟踪其指定路径或表面时运动协调;运动协调由路径或表面的机器人之间理想的参数偏移来界定;通过控制与路径或表面参数相对应的矢量场之间的虚拟坐标,实现这种预期的偏移;以动态系统理论和Lyapunov理论为支撑的严格数学保证,为所有最初位置上路径或表面的机器人的有效分布式运动协调和导航提供了依据;作为实用机器人应用的一个例子,我们从拟议的Dubins-car型模型的协调指导矢量场获得一种控制算法。我们提议的算法分布并可扩缩到任意数的机器人。此外,广泛的说明性模拟和固定翼飞机户外实验还验证了我们算法的有效性和稳健性。