OSQP

Open-source quadratic-program solver based on operator splitting, widely used in MPC and whole-body control.

OSQP is an open-source solver for quadratic programs (QPs) — optimization problems with a quadratic objective and linear inequality constraints. It was developed by researchers at Oxford and Stanford (Stellato, Banjac, Goulart, Bemporad, Boyd, and others), with the paper published in 2020. In robotics, model predictive control, whole-body control, and contact-force allocation are all commonly formulated as QPs that must be solved within a single control cycle, often just a few milliseconds. OSQP uses ADMM (Alternating Direction Method of Multipliers), an algorithm that splits a large problem into simpler subproblems solved in alternation. It's implemented in pure C with no external dependencies, supports warm-starting (using the previous time step's solution as the initial guess), and can generate embedded C code, which makes it well suited to real-time control. It also has Python, MATLAB, and C++ interfaces.

ExampleA quadruped robot's convex MPC controller formulates the foot-force optimization for the next ten steps as a QP on every control cycle, and solves it with warm-started OSQP in a few milliseconds.

Also called

Operator Splitting Quadratic Program solver

Related

Quadratic Programming · Model Predictive Control · Convex MPC · Whole-Body Control · qpOASES · Convex Optimization

Sources

OSQP 官网 (Chinese)
OSQP: an operator splitting solver for quadratic programs (arXiv)