标题： 多边形障碍物避让结合模型预测控制和模糊逻辑 显示英文标题

标题： Polygonal Obstacle Avoidance Combining Model Predictive Control and Fuzzy Logic

摘要： 在实际应用中，移动机器人在受限环境中的导航通常使用空间离散的成本图来表示障碍物。 路径跟踪是模型预测控制（MPC）的一个典型应用场景，但在这种情况下，制定避障约束具有挑战性。 通常，MPC问题的成本和约束被定义为显式函数，而典型的求解器在处理连续可微函数时效果最佳。 这与空间离散的占用网格地图相反，在占用网格地图中，网格的值定义了与占用相关的成本。 本文提出了一种方法，通过将占用网格地图重新表述为连续可微函数，以解决这种兼容性问题，并将其作为约束嵌入到MPC方案中。 每个障碍物被定义为一个多边形——半空间的交集。 任何半空间都是一个线性不等式，表示多边形的一条边。 使用AND和OR运算符，可以描述所有障碍物的集合，从而得到避障约束。 本文的主要贡献是利用模糊逻辑将包含逻辑运算符的约束重新表述为与标准MPC公式兼容的不等式约束。 基于MPC的轨迹规划器在仿真中成功进行了测试。 这一概念也可应用于导航任务之外，以在MPC中实现逻辑或语言约束。 显示英文摘要

摘要： In practice, navigation of mobile robots in confined environments is often done using a spatially discrete cost-map to represent obstacles. Path following is a typical use case for model predictive control (MPC), but formulating constraints for obstacle avoidance is challenging in this case. Typically the cost and constraints of an MPC problem are defined as closed-form functions and typical solvers work best with continuously differentiable functions. This is contrary to spatially discrete occupancy grid maps, in which a grid's value defines the cost associated with occupancy. This paper presents a way to overcome this compatibility issue by re-formulating occupancy grid maps to continuously differentiable functions to be embedded into the MPC scheme as constraints. Each obstacle is defined as a polygon -- an intersection of half-spaces. Any half-space is a linear inequality representing one edge of a polygon. Using AND and OR operators, the combined set of all obstacles and therefore the obstacle avoidance constraints can be described. The key contribution of this paper is the use of fuzzy logic to re-formulate such constraints that include logical operators as inequality constraints which are compatible with standard MPC formulation. The resulting MPC-based trajectory planner is successfully tested in simulation. This concept is also applicable outside of navigation tasks to implement logical or verbal constraints in MPC.