Sparse programming is an important tool in robotics, for example in real-time sparse inverse kinematic control with a minimum number of active joints, or autonomous goal selection. However, current approaches are limited to real-time control without consideration of the underlying non-linear problem. This prevents the application to non-linear problems like inverse kinematic planning while the robot autonomously chooses from a set of potential goal positions. Instead, kinematic reachability approximations are used while the robot's whole body motion is considered separately. Furthermore, the sparse constraints are not prioritized for intuitive problem formulation. Lastly, the computational effort of the used standard solvers is cubically dependent on the number of constraints which is problematic in the presence of a large number of possible goals. In this work, we address sparse hierarchical non-linear programs with tools from hierarchical non-linear programming to gain a holistic understanding of the problem at hand. The resulting sequential sparse hierarchical quadratic programming solver scales linearly in the number of constraints and enables the formulation of sparse non-linear equality and inequality constraints on any priority level without feasibility requirements. This enables efficient robot sparse hierarchical inverse kinematic planning and control with autonomous goal selection from a high number of possible goal positions without any reachability approximations.

翻译：稀疏规划是机器人学中的重要工具，例如在实现最少活动关节的实时稀疏逆运动学控制或自主目标选择中。然而，现有方法仅限于实时控制，未考虑底层的非线性问题。这阻碍了其在非线性问题（如机器人从一组潜在目标位置中自主选择时的逆运动学规划）中的应用。取而代之的是，现有方法使用运动学可达性近似，同时将机器人全身运动单独考虑。此外，稀疏约束未按优先级划分，不利于直观的问题表述。最后，所用标准求解器的计算量与约束数量的立方成正比，这在存在大量可能目标时会产生问题。本工作通过采用分层非线性规划工具来处理稀疏分层非线性规划问题，从而获得对当前问题的整体理解。所提出的序列稀疏分层二次规划求解器的计算复杂度与约束数量呈线性关系，并允许在任何优先级上表述稀疏非线性等式与不等式约束，且无需满足可行性要求。这使得机器人能够从大量可能目标位置中实现高效的稀疏分层逆运动学规划与控制，并完成自主目标选择，且无需任何可达性近似。