Trajectory optimization for mobile robots using model predictive control

The goal of this article is trajectory generation for biped robots based on Model Predictive Control (MPC) and the receding-horizon principle. Specifically, we want to minimize the error between the desired CoM and ZMP trajectory and the actual one and the cancellation of the shock gradient of the CoM and ZMP movements. Model predictive control (MPC) consist in a finite horizon optimal control scheme which uses a prediction model to predict vehicle response and future states, thus minimizing the current error and optimizing the future trajectory within the prediction horizon. The proposed algorithm will provide a trajectory of control inputs which will optimize the system states utilizing a quadratic form cost function similar to standard linear quadratic tracking. Specific to finite horizon control, the cost is summed over the finite prediction horizon of time length, rather than over an infinite time horizon. Many techniques have been proposed, developed, and applied to solve this constrained optimization problem for the mobile robots. With our aproach we try to investigate how is the MPC framework is applicable to trajectory generation for point-to-point problems with a fixed final time and to find a set of assumptions and methods that allow for real-time solutions.