Application of Nonlinear Model Predictive Control to Holonomic Mobile Robots without Terminal Constraints or Costs

Abstract

The use of mobile robots greatly enhances the capability and versatility of industrial robots compared to their fixed counterpart. However, successfully deploying autonomous mobile robots is challenging and requires accurate mapping, localization, planning and control. Herein, we focus the application of nonlinear model predictive control to a holonomic mobile robot while ensuring closed loop asymptotic stability. This thesis presents three main contributions in this area.

We begin with a study of the regulation control of a holonomic mobile robots with limits on acceleration under a Model Predictive Control (MPC) scheme without stabilizing terminal conditions or costs. Closed-loop asymptotic stability is ensured by suitably choosing the prediction horizon length. We first compute a set of admissible states for a holonomic mobile robot with limits on acceleration using the theory of barriers. Then, by deriving a growth (envelope) function for the MPC value function, we determine a stabilizing prediction horizon length. Theoretical results are confirmed through numerical simulations.

Next the Model Predictive Path Following Control (MPFC) of holonomic mobile robots is considered. Here, the control objective is to follow a geometric path, where the time evolution of the path parameterization is not fixed a priori, but rather is left as an extra degree of freedom for the controller. Contrary to previous works, we show that the asymptotic stability can be ensured for the resulting closed-loop system under MPFC without terminal constraints or costs. The analysis is based on verifying the cost-controllability assumption by deriving an upper bound on the MPFC finite-horizon value function. This bound is used to determine a stabilizing prediction horizon. The analysis is preformed in the discrete-time setting and results are verified by numerical simulations.

Finally, a dual-objective MPC algorithm for an open chain manipulator is presented, which, as a primary objective takes the end effector to a desired position and as a secondary goal minimizes the effort required from the actuators. To achieve this, a recursive Newton-Euler algorithm is used to calculate the system dynamics and to determine the actuator torques. The proposed method is based on a time varying cost function which, as time goes on, reduces weight on the secondary objective. This allows the controller to minimize torque at the start of the maneuver without affecting the ability of the system to reach the desired end effector position.

By taking advantage of the inherent benefits of MPC such as the ability to naturally incorporate constraints and to manipulate the objective function, the algorithms proposed here offer control solutions applicable in a variety of mobile robotic applications.