Modular reconfigurable manipulators enable quick adaptation and versatility to address different application environments and tailor to the specific requirements of the tasks. Task performance significantly depends on the manipulator's mounted pose and morphology design, therefore posing the need of methodologies for selecting suitable modular robot configurations and mounted pose that can address the specific task requirements and required performance. Morphological changes in modular robots can be derived through a discrete optimization process involving the selective addition or removal of modules. In contrast, the adjustment of the mounted pose operates within a continuous space, allowing for smooth and precise alterations in both orientation and position. This work introduces a computational framework that simultaneously optimizes modular manipulators' mounted pose and morphology. The core of the work is that we design a mapping function that \textit{implicitly} captures the morphological state of manipulators in the continuous space. This transformation function unifies the optimization of mounted pose and morphology within a continuous space. Furthermore, our optimization framework incorporates a array of performance metrics, such as minimum joint effort and maximum manipulability, and considerations for trajectory execution error and physical and safety constraints. To highlight our method's benefits, we compare it with previous methods that framed such problem as a combinatorial optimization problem and demonstrate its practicality in selecting the modular robot configuration for executing a drilling task with the CONCERT modular robotic platform.

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