Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control

Fast feedback control and safety guarantees are essential in modern robotics. We present an approach that achieves both by combining novel robust model predictive control (MPC) with function approximation via (deep) neural networks (NNs). The result is a new approach for complex tasks with nonlinear, uncertain, and constrained dynamics as are common in robotics. Specifically, we leverage recent results in MPC research to propose a new robust setpoint tracking MPC algorithm, which achieves reliable and safe tracking of a dynamic setpoint while guaranteeing stability and constraint satisfaction. The presented robust MPC scheme constitutes a one-layer approach that unifies the often separated planning and control layers, by directly computing the control command based on a reference and possibly obstacle positions. As a separate contribution, we show how the computation time of the MPC can be drastically reduced by approximating the MPC law with a NN controller. The NN is trained and validated from offline samples of the MPC, yielding statistical guarantees, and used in lieu thereof at run time. Our experiments on a state-of-the-art robot manipulator are the first to show that both the proposed robust and approximate MPC schemes scale to real-world robotic systems.Comment: 8 pages, 4 figures

Nonlinear model predictive low-level control

This dissertation focuses on the development, formalization, and systematic evaluation of a novel nonlinear model predictive control (MPC) concept with derivative-free optimization. Motivated by a real industrial application, namely the position control of a directional control valve, this control concept enables straightforward implementation from scratch, robust numerical optimization with a deterministic upper computation time bound, intuitive controller design, and offers extensions to ensure recursive feasibility and asymptotic stability by design. These beneficial controller properties result from combining adaptive input domain discretization, extreme input move-blocking, and the integration with common stabilizing terminal ingredients. The adaptive discretization of the input domain is translated into time-varying finite control sets and ensures smooth and stabilizing closed-loop control. By severely reducing the degrees of freedom in control to a single degree of freedom, the exhaustive search algorithm qualifies as an ideal optimizer. Because of the exponentially increasing combinatorial complexity, the novel control concept is suitable for systems with small input dimensions, especially single-input systems, small- to mid-sized state dimensions, and simple box-constraints. Mechatronic subsystems such as electromagnetic actuators represent this special group of nonlinear systems and contribute significantly to the overall performance of complex machinery. A major part of this dissertation addresses the step-by-step implementation and realization of the new control concept for numerical benchmark and real mechatronic systems. This dissertation investigates and elaborates on the beneficial properties of the derivative-free MPC approach and then narrows the scope of application. Since combinatorial optimization enables the straightforward inclusion of a non-smooth exact penalty function, the new control approach features a numerically robust real-time operation even when state constraint violations occur. The real-time closed-loop control performance is evaluated using the example of a directional control valve and a servomotor and shows promising results after manual controller design. Since the common theoretical closed-loop properties of MPC do not hold with input moveblocking, this dissertation provides a new approach for general input move-blocked MPC with arbitrary blocking patterns. The main idea is to integrate input move-blocking with the framework of suboptimal MPC by defining the restrictive input parameterization as a source of suboptimality. Finally, this dissertation extends the proposed derivative-free MPC approach by stabilizing warm-starts according to the suboptimal MPC formulation. The extended horizon scheme divides the receding horizon into two parts, where only the first part of variable length is subject to extreme move-blocking. A stabilizing local controller then completes the second part of the prediction. The approach involves a tailored and straightforward combinatorial optimization algorithm that searches efficiently for suboptimal horizon partitions while always reproducing the stabilizing warm-start control sequences in the nominal setup

Stability and performance in MPC using a finite-tail cost

In this paper, we provide a stability and performance analysis of model predictive control (MPC) schemes based on finite-tail costs. We study the MPC formulation originally proposed by Magni et al. (2001) wherein the standard terminal penalty is replaced by a finite-horizon cost of some stabilizing control law. In order to analyse the closed loop, we leverage the more recent technical machinery developed for MPC without terminal ingredients. For a specified set of initial conditions, we obtain sufficient conditions for stability and a performance bound in dependence of the prediction horizon and the extended horizon used for the terminal penalty. The main practical benefit of the considered finite-tail cost MPC formulation is the simpler offline design in combination with typically significantly less restrictive bounds on the prediction horizon to ensure stability. We demonstrate the benefits of the considered MPC formulation using the classical example of a four tank system

Approximate non-linear model predictive control with safety-augmented neural networks

Model predictive control (MPC) achieves stability and constraint satisfaction for general nonlinear systems, but requires computationally expensive online optimization. This paper studies approximations of such MPC controllers via neural networks (NNs) to achieve fast online evaluation. We propose safety augmentation that yields deterministic guarantees for convergence and constraint satisfaction despite approximation inaccuracies. We approximate the entire input sequence of the MPC with NNs, which allows us to verify online if it is a feasible solution to the MPC problem. We replace the NN solution by a safe candidate based on standard MPC techniques whenever it is infeasible or has worse cost. Our method requires a single evaluation of the NN and forward integration of the input sequence online, which is fast to compute on resource-constrained systems. The proposed control framework is illustrated on three non-linear MPC benchmarks of different complexity, demonstrating computational speedups orders of magnitudes higher than online optimization. In the examples, we achieve deterministic safety through the safety-augmented NNs, where naive NN implementation fails

Oracle-based economic predictive control

Article number 107434This paper presents an economic model predictive controller, under the assumption that the only mea- surable signal of the plant is the economic cost to be minimized. In order to forecast the evolution of this economic cost for a given input trajectory, a prediction model with a NARX structure, the so-called oracle, is proposed. Sufficient conditions to ensure the existence of such oracle are studied, proving that it can be derived for a general nonlinear system if the economic cost function is a Morse function. Based on this oracle, economic model predictive controllers are proposed, and their stability is demonstrated in nominal conditions under a standard dissipativity assumption. The viability of these controllers in practi- cal settings (where the oracle may provide imperfect predictions for generic inputs) is proven by means of input-to-state stability. These properties have been illustrated in a case study based on a continuously stirred tank reactorMinisterio de Economía y Competitividad (MINECO). España DPI2016-76493-C3-1-RAgencia Estatal de Investigación (AEI) PID2019-106212RB-C41/AEI/10.13039/50110001103

Analysis and design of model predictive control frameworks for dynamic operation -- An overview

This article provides an overview of model predictive control (MPC) frameworks for dynamic operation of nonlinear constrained systems. Dynamic operation is often an integral part of the control objective, ranging from tracking of reference signals to the general economic operation of a plant under online changing time-varying operating conditions. We focus on the particular challenges that arise when dealing with such more general control goals and present methods that have emerged in the literature to address these issues. The goal of this article is to present an overview of the state-of-the-art techniques, providing a diverse toolkit to apply and further develop MPC formulations that can handle the challenges intrinsic to dynamic operation. We also critically assess the applicability of the different research directions, discussing limitations and opportunities for further researc