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Hierarchical least-squares programs with linear constraints (HLSP) are a typeof optimization problem very common in robotics. Each priority level containsan objective in least-squares form which is subject to the linear constraintsof the higher priority levels. Active-set methods are a popular choice forsolving them. However, they can perform poorly in terms of computational timeif there are large changes of the active set. We therefore propose acomputationally efficient primal-dual interior-point method (IPM) for denseHLSP's which is able to maintain constant numbers of solver iterations in thesesituations. We base our IPM on the computationally efficient nullspace methodas it requires only a single matrix factorization per solver iteration insteadof two as it is the case for other IPM formulations. We show that the resultingnormal equations can be expressed in least-squares form. This avoids theformation of the quadratic Lagrangian Hessian and can possibly maintain highlevels of sparsity. Our solver reliably solves ill-posed instantaneoushierarchical robot control problems without exhibiting the large variations incomputation time seen in active-set methods.

$\mathcal{N}$IPM-HLSP: An Efficient Interior-Point Method for Hierarchical Least-Squares Programs