Math & Kinematics
Quadratic Program (QP)
A quadratic program (QP) is an optimization problem with a quadratic objective and linear constraints, convex and efficiently solvable when the objective's Hessian is positive semidefinite. Robotics runs QPs at control rates for whole-body control, inverse kinematics, contact force distribution, and control-barrier-function safety filters, using solvers such as OSQP, qpOASES, and ProxQP.
Why it matters for physical AI
The QP is the workhorse that turns high-level commands, including learned policy outputs, into constraint-satisfying joint torques hundreds of times per second on legged and manipulator systems.
Related terms
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