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Most reconfiguration planners for self-reconfiguring robots do not consider the placement of specific modules within the configuration. Recently, we have begun to investigate heterogeneous reconfiguration planning in lattice-based systems, in which there are various classes of modules. The start and goal configurations specify the class of each module, in addition to placement. Our previous work presents solutions for this problem with unrestricted free space available to the robot during reconfiguration, and also free space limited to a thin connected region over the entire surface of the configuration. In this paper, we further this restriction and define free space by an arbitrarily-shaped bounding region. This addresses the important problem of reconfiguration among obstacles, and reconfiguration over a rigid surface. Our algorithm plans module trajectories through the volume of the structure, and is divided into two phases: shape-forming, and sorting the goal configuration to correctly position modules by class. The worst-case running time for the first phase is O(n2) with O(n2) moves for an n-module robot, and a loose upper bound for the second phase is O(n4) time and moves. However, we show this bound to be Θ (n2)time and moves in common instances.