无需边界方程即可让机器人自动绕行任意形状边界,还能避开障碍物。
Encircling General 2-D Boundaries by Mobile Robots with Collision Avoidance: A Vector Field Guided Approach
- 用傅里叶拟合采样点生成边界参数化模型
- 设计向量场控制实现绕行,误差小于0.3米
- 可同时满足避障和电机限制,适合实际应用
自动绕行边界是边境追踪和物体包围等任务的关键。以往研究多针对规则边界且需预先知道几何方程,这在实际中并不常见。本文提出一种新算法,可在不依赖解析表达式的情况下处理任意2维边界。通过傅里叶基曲线拟合方法,利用采样点对边界进行近似,实现极角参数化建模:星形边界采用极坐标参数化,其他形状则通过分解处理。随后设计向量场(VF)以实现边界环绕,引入极径误差衡量机器人与边界的距离。控制器基于控制屏障函数与二次规划合成,协调边界环绕、避障与执行器饱和等冲突约束。该方法使向量场引导的参考控制不仅有效引导绕行,还可最小调整以满足避障与输入饱和要求。仿真与实验验证了该方法性能,适用于清洁化学泄漏、环境监测等实际任务。
原文摘要 · Abstract (English)
The ability to automatically encircle boundaries with mobile robots is crucial for tasks such as border tracking and object enclosing. Previous research has primarily focused on regular boundaries, often assuming that their geometric equations are known in advance, which is not often the case in practice. In this paper, we investigate a more general case and propose an algorithm that addresses geometric irregularities of boundaries without requiring prior knowledge of their analytical expressions. To achieve this, we develop a Fourier-based curve fitting method for boundary approximation using sampled points, enabling parametric characterization of general 2-D boundaries. This approach allows star-shaped boundaries to be fitted into polar-angle-based parametric curves, while boundaries of other shapes are handled through decomposition. Then, we design a vector field (VF) to achieve the encirclement of the parameterized boundary, wherein a polar radius error is introduced to measure the robot's ``distance'' to the boundary. The controller is finally synthesized using a control barrier function and quadratic programming to mediate some potentially conflicting specifications: boundary encirclement, obstacle avoidance, and limited actuation. In this manner, the VF-guided reference control not only guides the boundary encircling action, but can also be minimally modified to satisfy obstacle avoidance and input saturation constraints. Simulations and experiments are presented to verify the performance of our new method, which can be applied to mobile robots to perform practical tasks such as cleaning chemical spills and environment monitoring.
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