用优化方法让机器人全身协同抓物，效率比现有方法快77%。

Daily tasks require us to use our whole body to manipulate objects, for instance when our hands are unavailable. We consider the issue of providing humanoid robots with the ability to autonomously perform similar whole-body manipulation tasks. In this context, the infinite possibilities for where and how contact can occur on the robot and object surfaces hinder the scalability of existing planning methods, which predominantly rely on discrete sampling. Given the continuous nature of contact surfaces, gradient-based optimization offers a more suitable approach for finding solutions. However, a key remaining challenge is the lack of an efficient representation of robot surfaces. In this work, we propose (i) a representation of robot and object surfaces that enables closed-form computation of proximity points, and (ii) a cost design that effectively guides whole-body manipulation planning. Our experiments demonstrate that the proposed framework can solve problems unaddressed by existing methods, and achieves a 77% improvement in planning time over the state of the art. We also validate the suitability of our approach on real hardware through the whole-body manipulation of boxes by a humanoid robot.