Quadratic Programming Optimization Applied to Robotics Systems

Reactive kinematic control in velocity space is closely related to the Jacobian presented in the system. However, if the Jacobian is rank-deficient, certain task-space velocities become unachievable, leading to controller degradation. This work presents an approach to controlling robotic systems based on a quadratic programming formulation that yields solutions in just a few milliseconds. The proposed framework is tested in simulation using a two-link planar robotic arm and a mobile robot. Simulations are implemented in MuJoCo and Webots, respectively, to demonstrate the efficiency of the formulation.