We develop an autonomous navigation algorithm for a robot operating in two-dimensional environments containing obstacles, with arbitrary non-convex shapes, which can be in close proximity with each other, as long as there exists at least one safe path connecting the initial and the target location. An instrumental transformation that modifies (virtually) the non-convex obstacles, in a non-conservative manner, is introduced to facilitate the design of the obstacle-avoidance strategy. The proposed navigation approach relies on a hybrid feedback that guarantees global asymptotic stabilization of a target location while ensuring the forward invariance of the modified obstacle-free workspace. The proposed hybrid feedback controller guarantees Zeno-free switching between the move-to-target mode and the obstacle-avoidance mode based on the proximity of the robot with respect to the modified obstacle-occupied workspace. Finally, we provide an algorithmic procedure for the sensor-based implementation of the proposed hybrid controller and validate its effectiveness via some numerical simulations.

翻译：我们针对在包含任意非凸形状障碍物的二维环境中运行的机器人，提出了一种自主导航算法。只要初始位置与目标位置之间存在至少一条安全路径，即使障碍物彼此紧密邻近，该算法依然有效。我们引入了一种非保守的虚拟变换，以（虚拟地）修改非凸障碍物，从而便于设计避障策略。所提出的导航方法依赖于一种混合反馈机制，该机制能够在保证修改后的无障碍工作空间正向不变性的同时，实现目标位置的全局渐近镇定。该混合反馈控制器根据机器人相对于修改后的障碍物占据空间的邻近程度，确保在“向目标移动”模式与“避障”模式之间实现无芝诺现象的切换。最后，我们给出了该混合控制器基于传感器实现的一种算法步骤，并通过数值模拟验证了其有效性。