Model Predictive Control of Nonholonomic Mobile Robots Without Stabilizing Constraints and Costs

Robust RHC for wheeled vehicles with bounded disturbances

“…Due to the advantages in handling physical constraints and optimizing control performance, the receding horizon control (RHC), also referred to as model predictive control (MPC), has been widely employed in various applications for constrained systems, eg, chemicals, food processing, automotive, and aerospace applications, surveyed by Qin and Badgwell . Examples of RHC application for unmanned vehicles include the air/ground traffic control management, the motion/trajectory planning for the vehicles, and the tracking and/or regulation of vehicles . In these problems, the motions and/or trajectories of vehicles need to be planed to achieve the desired objective in some optimal senses, and some given physical constraints (eg, the collision avoidance constraint, the velocity constraint, and the input saturation constraint) need to be satisfied.…”

“…Therefore, the RHC strategy is preferred by the researchers to others (eg, sliding mode control, dynamic feedback linearization, backstepping technique, etc), and more and more approaches emerge to be effective solutions for these problems. Some of these emerged approaches are proposed in synthesis framework (ie, both the recursive feasibility and stability are guaranteed) for the control of unmanned vehicles . Following the common practice of RHC synthesis approach in the work of Mayne et al, choosing a proper terminal (penalty) cost, developing a terminal‐state region (or terminal constraint set) with (robustly) positive invariance, and designing an associated controller are the three key ingredients.…”

“…As the (robust) positively invariant terminal constraint set and associated control law are successfully developed, the approaches proposed by Fontes can fall in synthesis category. To avoid the challenge of developing positively invariant terminal constraint set, an alternative RHC synthesis approach can be presented without stabilizing constraints and costs, where the asymptotic stability depends much on the prediction horizon. Unfortunately, the aforementioned synthesis approaches cannot be applied for tracking case because their associated control laws (or control input candidates) are designed only for stationary reference.…”

“…1 Examples of RHC application for unmanned vehicles include the air/ground traffic control management, 2,3 the motion/trajectory planning for the vehicles, 4,5 and the tracking and/or regulation of vehicles. [6][7][8][9][10] In these problems, the motions and/or trajectories of vehicles need to be planed to achieve the desired objective in some optimal senses, and some given physical constraints (eg, the collision avoidance constraint, the velocity constraint, and the input saturation constraint) need to be satisfied. Therefore, the RHC strategy is preferred by the researchers to others (eg, sliding mode control, 11 dynamic feedback linearization, 12 backstepping technique, 13 etc), and more and more approaches emerge to be effective solutions for these problems.…”

“…Some of these emerged approaches are proposed in synthesis framework (ie, both the recursive feasibility and stability are guaranteed) for the control of unmanned vehicles. 8,10,14 Following the common practice of RHC synthesis approach in the work of Mayne et al, 15 choosing a proper terminal (penalty) cost, developing a terminal-state region (or terminal constraint set) with (robustly) positive invariance, and designing an associated controller are the three key ingredients.…”