We present a sequential hierarchical least-squares programming solver with trust-region and hierarchical step-filter tailored to prioritized non-linear optimal control. It is based on a hierarchical step-filter which resolves each priority level of a non-linear hierarchical least-squares programming via a globally convergent sequential quadratic programming step-filter. Leveraging a condition on the trust-region or the filter initialization, our hierarchical step-filter maintains this global convergence property. The hierarchical least-squares programming sub-problems are solved via a sparse nullspace method based interior point method. It is based on an efficient implementation of the turnback algorithm for the computation of nullspace bases for banded matrices. It is also here that we propose a nullspace trust region adaptation method towards a comprehensive hierarchical step-filter. We demonstrate the computational efficiency of the hierarchical solver on typical test functions like the Rosenbrock and Himmelblau's functions, inverse kinematics problems and optimal control.

翻译：摘要：我们提出了一种结合信赖域与分层步长滤波器的序列分层最小二乘规划求解器，专为优先级非线性最优控制设计。该求解器基于分层步长滤波器，通过全局收敛的序列二次规划步长滤波器解析非线性分层最小二乘规划中的每个优先级层级。通过利用信赖域或滤波器初始化的条件，我们的分层步长滤波器保持了全局收敛性。分层最小二乘规划子问题通过基于稀疏零空间法的内点法求解，其核心在于采用高效的回溯算法计算带状矩阵的零空间基。同时，我们在此提出一种零空间信赖域自适应方法，以构建完备的分层步长滤波器。通过在Rosenbrock和Himmelblau函数等典型测试函数、逆运动学问题及最优控制中的计算实验，验证了该分层求解器的计算效率。