机器人配置空间中异构约束的可行性距离场
Feasibility Distance Fields for Heterogeneous Constraints in Robot Configuration Space
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中文总结 AI 辅助
本文提出可行性距离场（FDF），在统一关节空间度量下度量到不可行配置集的距离，支持异构约束组合，并通过神经近似在UR5e和双臂仿真中验证其精度与有效性。
中文摘要 AI 辅助
机器人操作臂受到特定约束指标的监控，这些指标的单位和梯度尺度不可比较，因此它们无法提供在违反约束之前剩余配置空间运动的通用度量。我们将可行性距离场（FDF）定义为在固定正定关节空间度量下，到不可行配置集并集的距离。经典的距离到集合理论给出了1-Lipschitz连续性、几乎处处可微性，以及在最近投影唯一处单位对偶梯度范数。机器人学的贡献在于可容许性分析，表明实际约束何时定义非空闭集。我们推导了外部碰撞和自碰撞、关节极限、灵巧度、笛卡尔空间和任务投影柔顺性、负载下关节扭矩以及动态可操作性的可容许公式。由于每个场使用相同的度量，异构约束通过逐点最小值组合，条件约束保留固定距离空间，多机器人约束产生块稀疏梯度，识别哪些机器人必须响应。我们生成基于投影的标签，并使用距离损失和Eikonal惩罚训练神经近似。在UR5e和双臂单元上的仿真评估了七个场，使用值、投影、符号、梯度、组合和移动障碍物诊断。在8000个配置中，最大可行侧正割比为0.920，平均学习梯度范数范围从0.994到0.998，投影残差范围从0.011到0.034弧度。在24条随机障碍物路径中，外部和组合碰撞场在3厘米内分别达到90.4%和91.6%的成功率，符号错误率低于2%。结果支持通用配置空间裕度，并识别出靠近中轴和稀疏采样边界处的近似误差。
英文摘要
Robot manipulators are monitored by constraint-specific indicators whose units and gradient scales are not comparable, so they do not provide a common measure of the configuration-space motion remaining before violation. We define the feasibility distance field (FDF) as the distance, under a fixed positive-definite joint-space metric, to the union of infeasible configuration sets. Classical distance-to-set theory gives 1-Lipschitz continuity, almost-everywhere differentiability, and unit dual-gradient norm wherever the nearest projection is unique. The robotics contribution is an admissibility analysis showing when practical constraints define non-empty closed sets. We derive admissible formulations for external and self-collision, joint limits, dexterity, Cartesian and task-projected compliance, joint torque under payload, and dynamic manipulability. Since every field uses the same metric, heterogeneous constraints compose by a pointwise minimum, conditioned constraints retain a fixed distance space, and multi-robot constraints produce block-sparse gradients that identify which robots must react. We generate projection-based labels and train neural approximations with a distance loss and an Eikonal penalty. Simulations on a UR5e and a dual-arm cell evaluate seven fields using value, projection, sign, gradient, composition, and moving-obstacle diagnostics. Across 8,000 configurations, the largest feasible-side secant ratio is 0.920, mean learned gradient norms range from 0.994 to 0.998, and projection residuals range from 0.011 to 0.034 rad. Across 24 random obstacle paths, the external and composed collision fields achieve 90.4% and 91.6% success within 3 cm, with sign-error rates below 2%. The results support a common configuration-space margin and identify approximation errors near medial axes and sparsely sampled boundaries.
