Hierarchical Quadratic Programming

Solving multiple control objectives in strict priority order, layer by layer, so lower priorities never interfere with higher ones.

Robots often need to satisfy several potentially conflicting objectives at once: don't fall over, don't let feet slip, reach the target with the hand, stay within joint limits. A weighted QP multiplies each by a weight and sums them into one cost, which can only produce a compromise, and an important task can still get sacrificed. HQP instead orders them strictly: solve the highest-priority quadratic program first, treat its set of optimal solutions as a constraint, then solve the next layer within the remaining degrees of freedom (the null space) — so lower layers can never break a higher layer's result. It generalizes the classic null-space projection method, with the difference that every layer here can carry inequality constraints too (joint limits, friction cones, etc.). Escande, Mansard, and Wieber's 2014 IJRR paper gave a fast solver supporting both equality and inequality constraints at every layer, capable of generating whole-body motion for the HRP-2 humanoid at control-loop rates; it's commonly used for inverse kinematics or inverse dynamics solves within whole-body control.

ExampleA humanoid reaching for a distant object: layer 1 keeps the support foot planted and the center of mass inside the support polygon; layer 2 gets the hand to the target; layer 3 orients the head toward the object and returns other joints to a default posture. If the reach isn't possible, it's the lower layers that get sacrificed, not balance.

Also called

HQP, Hierarchical QP

Related

Task Prioritization · Whole-Body Control · Quadratic Programming · Null-Space Control · Operational Space Control · Inverse Kinematics (IK)

Sources

Escande, Mansard, Wieber, Hierarchical Quadratic Programming: Fast Online Humanoid-Robot Motion Generation (IJRR 2014)