Using Model Predictive Control for Local Navigation of Mobile Robots

Abstract

Model predictive control, MPC, has many interesting features for its application to mobile robot control. It is a more effective advanced control technique, as compared to the standard PID control, and has made a significant impact on industrial process control (Maciejowski, 2002). MPC usually contains the following three ideas: • The model of the process is used to predict the future outputs along a horizon time. • An index of performance is optimized by a control sequence computation. • It is used a receding horizon idea, so at each instant of time the horizon is moved towards the future. It involves the application of the first control signal of the sequence computed at each step. The majority of the research developed using MPC techniques and their application to WMR (wheeled mobile robots) is based on the fact that the reference trajectory is known beforehand (Klancar & Skrjanc, 2007). The use of mobile robot kinematics to predict future system outputs has been proposed in most of the different research developed (Kuhne et al., 2005; Gupta et al., 2005). The use of kinematics have to include velocity and acceleration constraints to prevent WMR of unfeasible trajectory-tracking objectives. MPC applicability to vehicle guidance has been mainly addressed at path-tracking using different on-field fixed trajectories and using kinematics models. However, when dynamic environments or obstacle avoidance policies are considered, the navigation path planning must be constrained to the robot neighborhood where reactive behaviors are expected (Fox et al., 1997; Ogren & Leonard, 2005). Due to the unknown environment uncertainties, short prediction horizons have been proposed (Pacheco et al., 2008). In this context, the use of dynamic input-output models is proposed as a way to include the dynamic constraints within the system model for controller design. In order to do this, a set of dynamic models obtained from experimental robot system identification are used for predicting the horizon of available coordinates. Knowledge of different models can provide information about the dynamics of the robot, and consequently about the reactive parameters, as well as the safe stop distances. This work extends the use of on-line MPC as a suitable local path-tracking methodology by using a set of linear time-varying descriptions of the system dynamics when short prediction horizons are used. In the approach presented, the trajectory is dynamically updated by giving a straight line to be tracked. In this way, the control law considers the local point to be achieved and the WMR coordinates. The cost function is formulated with parameters that involve the capacity of turning and going straight. In the