Slovakia

Mecanum-wheeled robots have been thoroughly used to automate tasks in many different applications. However, they are usually controlled by neglecting their dynamics and relying only on their kinematic model. In this paper, we model the behaviour of such robots by taking into account both their equations of motion and the electrodynamic response of their actuators, including dry and viscous friction at their shafts. This allows us to design a model predictive controller aimed to minimise the energy consumed by the robot. The controller also satisfies a number of non-linear inequalities modelling motor voltage limits and obstacle avoidance constraints. The result is an agile controller that can quickly adapt to changes in the environment, while generating fast and energy-efficient manoeuvres towards the goal.

Nonlinear Model Predictive Control Conference 2021

Model Predictive Control for a Mecanum-Wheeled Robot Navigating among Obstacles

directional sliding wheels.

mecanum wheels

obstacle avoidance

optimization-based control

trajectory and path planning

mobile robot

motion control

dynamic modelling of wheeled robots

model predictive control

energy efficiency

The IFAC Conference on Nonlinear Model Predictive Control (NMPC 2021) aims to bring together researchers interested in and work in the MPC field from both academia and industry. This allows us to reflect and establish the current state-of-the-art and focus on the future development of the MPC field towards relevant directions.

Model predictive control (MPC) is indisputably one of the advanced control techniques that have significantly affected control engineering practice with thousands of controllers implemented in various fields, spanning from the process industry to automotive and robotics. This is due to its unique ability to handle constraints, take preview information about disturbances and setpoint changes into account, and optimize performance. Furthermore, MPC allows the consideration of various types of dynamics, from linear to nonlinear, discrete to continuous, as well as an online adaptation of models and parameters. The research community on MPC is very active, with hundreds of papers published every year. Over the past decades, many theoretical, as well as implementation results, have been achieved.

### **All content presented at NMPC2021, including videos, papers and slides will be available only to registered (regular/student) participants. The content can be accessed until August 31st, 2021.**



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The IFAC Conference on Nonlinear Model Predictive Control (NMPC 2021) aims to bring together researchers interested in and work in the MPC field from both academia and industry. This allows us to reflect and establish the current state-of-the-art and focus on the future development of the MPC field towards relevant directions.

technical paper

We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems.

Deep Learning Explicit Differentiable Predictive Control Laws for Buildings

We present a model predictive control (MPC) scheme to control linear time-invariant systems using only measured input-output data and no model knowledge. The scheme includes a terminal cost and a terminal set constraint on an extended state containing past input-output values. We provide an explicit design procedure for the corresponding terminal ingredients that only uses measured input-output data. Further, we prove that the MPC scheme based on these terminal ingredients exponentially stabilizes the desired setpoint in closed loop. Finally, we illustrate the advantages over existing data-driven MPC approaches with a numerical example.

On the Design of Terminal Ingredients for Data-Driven MPC

We develop an efficient algorithmic implementation of output feedback control of discrete-time linear systems with state and input constraints that is based on model predictive control (MPC) and moving horizon estimation (MHE). We present an iteration scheme which combines previously proposed proximity-based MHE and relaxed barrier function based MPC algorithms in a certainty equivalence output feedback fashion. The resulting overall closed-loop system is shown to converge to the origin under mild assumptions and simulation examples are used to demonstrate the advantages of the proposed approach.

Anytime MHE-Based Output Feedback MPC

Designing predictive controllers for systems with computationally limited embedded hardware, e.g. for autonomous vehicles, requires solving an optimization problem in real-time taking the vehicle dynamics and constraints into account.

Continuous-Time Approximated Parametric Output-Feedback Nonlinear Model Predictive Control

**Read paper on the following link:**

https://drive.google.com/file/d/10Ja3BWljpdOVUSBzNBzD-RJgnxp0Z-fD/view?usp=sharing

**Abstract:**



State and Parameter Estimation for Model-Based Retinal Laser Treatment

This paper presents an approach to design nonlinear control policies for the class of systems with nonlinear steady-state characteristics while assuming constant dynamic behavior. We present an approach where the nonlinear steady-state characteristics are approximated with a nonlinear function. Such a model then serves as the design model for the nonlinear model predictive control strategy. The validity of such a control approach is experimentally implemented on a laboratory scale device.

Nonlinear MPC Policy for Systems with Data Driven Identification

Model predictive control (MPC) is a powerful trajectory

Reinforcement Learning of the Prediction Horizon in Model Predictive Control

In the Economic Nonlinear Model Predictive (ENMPC) context, closed-loop stability relates to the existence of a storage function satisfying a dissipation inequality. Finding the storage function is in general-- for nonlinear dynamics and cost-- challenging, and has attracted attentions recently. Q-Learning is a well-known Reinforcement Learning (RL) techniques that attempts to capture action-value functions based on the state-input transitions and stage cost of the system. In this paper, we present the use of the Q-Learning approach to obtain the storage function and verify the dissipativity for discrete-time systems subject to state-input constraints. We show that undiscounted Q-learning is able to capture the storage function for dissipative problems when the parameterization is rich enough. The efficiency of the proposed method will be illustrated in the different case studies.

Verification of Dissipativity and Evaluation of Storage Function in Economic Nonlinear MPC Using Q-Learning

Many processes operate repetitively, for example, batch processes in biotechnology or chemical engineering. We propose a method for risk-aware run-to-run optimization and model predictive control of repetitive processes with uncertain models. The goal is to increase the performance as the number of runs increases by improving the model despite limited measurements while considering model uncertainty and avoiding uncertain areas. The method uses a gray-box model, i.e. a model formed by a first principle and a machine learning component, in this case, an artificial neural network. The model uncertainty might be large, particularly in the first runs, where only a few measurements are available. We propose to quantify this uncertainty using Bayesian inference. This is in turn reflected by a risk measure entering an open-loop optimal control problem and a shrinking-horizon Model Predictive Controller as a constraint to limit control and exploitation in high-risk areas. We show that using this risk measure we are able to efficiently reach high process performance. The proposed method is tested in simulations on two biotechnological fed-batch processes.

Towards Risk-Aware Machine Learning Supported Model Predictive Control and Open-Loop Optimization for Repetitive Processes

Often, systems need to adapt their behavior to other systems in their surroundings while obeying constraints to achieve good performance or due to safety reasons. We consider repetitive applications, where the reference for the controller stems from noisy sensor data. Including preview information of the reference, e.g. extrapolating from previous cycles or similar instances, can significantly improve the overall tracking performance and ensure constraint satisfaction.

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Model Predictive Control for a Mecanum-Wheeled Robot Navigating among Obstacles

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