Large-scale surface-following tasks require mobile manipulators when the work surface exceeds the workspace of a fixedbase manipulator. Base placement must consider not only inverse kinematic reachability but also collision feasibility and joint-space continuity along the task-point sequence. This paper proposes a grid-based base placement framework for these tasks. Task points and target poses are generated from a stereolithography (STL) mesh. For each predefined base candidate, inverse kinematics and collision checks are performed, and feasible task points and their corresponding joint solutions are stored for base assignment. Joint-space discontinuity is evaluated from joint variations between adjacent task points and incorporated into the base selection cost together with the number of base changes and planar travel distance. MATLAB simulations were conducted on a vehicle roof model. Of 885 task points, 853 had collision-free inverse kinematic solutions across the predefined set of 35 base candidates, and the proposed method assigned all 853 feasible points. Compared with a collision-aware baseline method, the proposed method reduced the number of joint discontinuities from 1 to 0, the maximum joint variation from 3.071 to 0.482 rad, the number of base changes from 22 to 9, and the planar base travel distance from 13.60 to 3.54 m.
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