Mobile manipulators promise agile, long-horizon behavior by coordinating base and arm motion, yet whole-body trajectory optimization in cluttered, confined spaces remains difficult due to high-dimensional nonconvexity and the need for fast, accurate collision reasoning. Configuration Space Distance Fields (CDF) enable fixed-base manipulators to model collisions directly in configuration space via smooth, implicit distances. This representation holds strong potential to bypass the nonlinear configuration-to-workspace mapping while preserving accurate whole-body geometry and providing optimization-friendly collision costs. Yet, extending this capability to mobile manipulators is hindered by unbounded workspaces and tighter base-arm coupling. We lift this promise to mobile manipulation with Generalized Configuration Space Distance Fields (GCDF), extending CDF to robots with both translational and rotational joints in unbounded workspaces with tighter base-arm coupling. We prove that GCDF preserves Euclidean-like local distance structure and accurately encodes whole-body geometry in configuration space, and develop a data generation and training pipeline that yields continuous neural GCDFs with accurate values and gradients, supporting efficient GPU-batched queries. Building on this representation, we develop a high-performance sequential convex optimization framework centered on GCDF-based collision reasoning. The solver scales to large numbers of implicit constraints through (i) online specification of neural constraints, (ii) sparsity-aware active-set detection with parallel batched evaluation across thousands of constraints, and (iii) incremental constraint management for rapid replanning under scene changes.

翻译：移动机械臂通过协调基座与手臂的运动，有望实现灵活、长时域的行为，但在杂乱、受限空间中进行全身轨迹优化仍然困难，这源于高维非凸性以及对快速、准确碰撞推理的需求。构型空间距离场使固定基座机械臂能够通过平滑的隐式距离直接在构型空间中建模碰撞。这种表示法具有巨大潜力，可以绕过从构型到工作空间的非线性映射，同时保留精确的全身几何结构并提供对优化友好的碰撞代价。然而，将这种能力扩展到移动机械臂受到无界工作空间和更紧密的基座-手臂耦合的阻碍。我们通过广义构型空间距离场将这一前景提升到移动操作领域，将CDF扩展到具有平移和旋转关节、工作空间无界且基座-手臂耦合更紧密的机器人。我们证明了GCDF保留了类欧几里得局部距离结构，并在构型空间中精确编码了全身几何，并开发了一个数据生成与训练流程，可产生具有精确值和梯度的连续神经GCDF，支持高效的GPU批量查询。基于此表示法，我们开发了一个以基于GCDF的碰撞推理为核心的高性能序列凸优化框架。该求解器通过以下方式扩展到大量隐式约束：(i) 神经约束的在线设定，(ii) 稀疏感知的主动集检测，在数千个约束上进行并行批量评估，以及 (iii) 增量式约束管理，以在场景变化下实现快速重规划。