Abstract
In this paper, a stochastic model predictive control (MPC) is proposed for the wheeled mobile robot to track a reference trajectory within a finite task horizon. The wheeled mobile robot is supposed to subject to additive stochastic disturbance with known probability distribution. It is also supposed that the mobile robot is subject to soft probability constraints on states and control inputs. The nonlinear mobile robot model is linearized and discretized into a discrete linear time-varying model, such that the linear time-varying MPC can be applied to forecast and control its future behavior. In the proposed stochastic MPC, the cost function is designed to penalize its tracking error and energy consumption. Based on quantile techniques, a learning-based approach is applied to transform the probability constraints to deterministic constraints, and to calculate the terminal constraint to guarantee recursive feasibility. It is proved that, with the proposed stochastic MPC, the tracking error of the closed-loop system is asymptotically average bounded. A simulation example is provided to support the theoretical result.
Highlights
Model predictive control (MPC) is a useful tool when dealing with stabilization or tracking problem with constraints
This paper presents a stochastic model predictive control (MPC) method for wheeled mobile robots based on framework of Hewing et al (2020)
A stochastic MPC is proposed for the wheeled mobile robot subject to probability constraints and stochastic disturbance to track its reference trajectory within the task horizon
Summary
Model predictive control (MPC) is a useful tool when dealing with stabilization or tracking problem with constraints. Violations of constraints are permitted in a predetermined level and the soft constraints can balance system performance and limits on states in the meantime Such characteristic renders stochastic MPC a promising method in a wide range of applications in energy or under actuated systems (Farina et al, 2016), such as energy scheduling (Rahmani-andebili and Shen, 2017), (Scarabaggio et al, 2021), (Jørgensen et al, 2016), energy management for vehicles (Cairano et al, 2014), temperature control in buildings (Hewing and Zeilinger, 2018), racing car Carrau et al (2016), quadrotors (Yang et al, 2017), overhead cranes. The main contribution is to develop a stochastic MPC method to forecast and control the wheeled mobile robot to track its reference trajectory against constraints and additive random disturbance with known distributions.
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