Real-time Whole-Body Motion Planning for Mobile Manipulators Carrying Arbitrarily Shaped Payloads via Kinematically-Coupled SVSDF

Mobile manipulators are increasingly tasked with transporting large, non-convex payloads through cluttered environments, yet existing planners either oversimplify the payload geometry or fail to handle the kinematic coupling between manipulator links, leading to lost feasible space or stalled optimization. This letter presents a real-time whole-body motion planning framework for mobile manipulators carrying arbitrarily shaped payloads. The front-end employs a chain-decomposed kernel-based collision check that preserves the true geometry of the robot and payload, with compact storage and fast bit-level queries. A mid-end preprocessing stage converts the front-end path into a continuous trajectory enforcing smoothness and feasibility, and executes it directly when collision-free to bypass the costly back-end. When refinement is required, the back-end performs trajectory optimization built on a Kinematically-Coupled SVSDF (KC-SVSDF), which propagates collision-avoidance gradients along the kinematic chain to produce coherent whole-body escape directions. Ablation studies, comparative benchmarks against state-of-the-art baselines, and real-world experiments on a differential-drive mobile manipulator demonstrate that the proposed framework reliably transports large, non-convex payloads through tight passages and cluttered environments.