This work presents a novel and efficient nonlinear programming framework that tightly integrates hierarchical decision-making with whole-body inverse kinematic planning and control. Decision-making plays a central role in many aspects of robotics, from sparse inverse kinematic control with a minimal number of joints, to inverse kinematic planning while simultaneously selecting a discrete end-effector location from multiple candidates. Current approaches often rely on heavy computations using mixed-integer nonlinear programming, separate decision-making from inverse kinematics (some times approximated by reachability methods), or employ efficient but less versatile $\ell_1$-norm formulations of linear sparse programming, without addressing the underlying nonlinear problem formulations. In contrast, the proposed sparse hierarchical nonlinear programming solver is efficient, versatile, and accurate by exploiting sparse hierarchical structure and leveraging the $\ell_0$-norm which is rarely used in robotics. The solver efficiently tackles complex nonlinear hierarchical decision-making problems previously unaddressed in the literature, such as inverse kinematic planning with simultaneous prioritized selection of end-effector locations from a large set of candidates, or inverse kinematic control with simultaneous selection of bi-manual grasp locations on a randomly rotated box.

翻译：本文提出了一种新颖且高效的非线性规划框架，该框架将分层决策与全身逆运动学规划及控制紧密结合。决策在机器人学的诸多方面扮演核心角色，从使用最少关节数量的稀疏逆运动学控制，到同时从多个候选末端执行器位置中选择离散位置的逆运动学规划。当前的方法通常依赖于使用混合整数非线性规划进行繁重计算，将决策与逆运动学分离（有时通过可达性方法近似），或采用线性稀疏规划中高效但通用性较弱的$\ell_1$范数形式，而未能解决底层的非线性问题表述。相比之下，所提出的稀疏分层非线性规划求解器通过利用稀疏分层结构并借助机器人学中极少使用的$\ell_0$范数，实现了高效、通用且精确的性能。该求解器有效处理了文献中此前未解决的复杂非线性分层决策问题，例如在从大量候选末端执行器位置中同时进行优先级选择的逆运动学规划，或在随机旋转的盒子上同时选择双臂抓取位置的逆运动学控制。