  This paper presents a state-of-the-art optimal controller for quadruped
locomotion. The robot dynamics is represented using a single rigid body (SRB)
model. A linear time-varying model predictive controller (LTV MPC) is proposed
by using linearization schemes. Simulation results show that the LTV MPC can
execute various gaits, such as trot and crawl, and is capable of tracking
desired reference trajectories even under unknown external disturbances. The
LTV MPC is implemented as a quadratic program using qpOASES through the CasADi
interface at 50 Hz. The proposed MPC can reach up to 1 m/s top speed with an
acceleration of 0.5 m/s2 executing a trot gait. The implementation is available
at https:// github.com/AndrewZheng-1011/Quad_ConvexMPC
