This paper proposes a novel model predictive control method with velocity estimation simultaneously constraining trajectory and velocity tracking errors for a cushion robot.The authors investigated a path planning method using improved particle swarm optimization (PSO) combined with Dijkstra's algorithm and obtained a real-time desired optimal motion path for obstacle avoidance.The authors designed a velocity observer to estimate the unmeasurable speed,while the asymptotic stability of the observer error system was established.A predictive controller with error-constrained performance was derived by solving a quadratic programming problem with incremental control.Simulation and experimental results confirm the effectiveness of the proposed method and verify that the error constraints adopted in the cushion robot provide safe motion while avoiding obstacles.