We present a Model Predictive Control (MPC) strategy for unknown input-affine nonlinear dynamical systems. A non-parametric method is used to estimate the nonlinear dynamics from observed data. The estimated nonlinear dynamics are then linearized over time varying regions of the state space to construct an Affine Time Varying (ATV) model. Error bounds arising from the estimation and linearization procedure are computed by using sampling techniques. The ATV model and the uncertainty sets are used to design a robust Model Predictive Control (MPC) problem which guarantees safety for the unknown system with high probability. A simple nonlinear example demonstrates the effectiveness of the approach where commonly used linearization methods fail.
Learning Hybrid Policies for MPC with Application to Drone Flight in Unknown Dynamic Environments
National Key Lab of Autonomous Intelligent Unmanned Systems, Beijing Institute of Technology（北京理工大学自主智能无人系统全国重点实验室）；Beijing Institute of Technology Chongqing Innovation Center（北京理工大学重庆创新中心）；Department of Control Science and Engineering, Tongji University（同济大学控制科学与工程系）
Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environments
Continental Automotive Technologies GmbH, Germany（德国大陆汽车技术有限公司）；Technical University of Berlin, Germany（柏林技术大学）；Free University of Berlin, Germany（柏林自由大学）
Modern robotic systems are endowed with superior mobility and mechanical skills that make them suited to be employed in real-world scenarios, where interactions with heavy objects and precise manipulation capabilities are required. For instance, legged robots with high payload capacity can be used in disaster scenarios to remove dangerous material or carry injured people. It is thus essential to develop planning algorithms that can enable complex robots to perform motion and manipulation tasks accurately. In addition, online adaptation mechanisms with respect to new, unknown environments are n…
Arizona State University（亚利桑那州立大学）；Toyota Research Institute of North America（丰田北美研究院）
In this paper, we present a decentralized control approach based on a Nonlinear Model Predictive Control (NMPC) method that employs barrier certificates for safe navigation of multiple nonholonomic wheeled mobile robots in unknown environments with static and/or dynamic obstacles. This method incorporates a Learned Barrier Function (LBF) into the NMPC design in order to guarantee safe robot navigation, i.e., prevent robot collisions with other robots and the obstacles. We refer to our proposed control approach as NMPC-LBF. Since each robot does not have a priori knowledge about the obstacles a…
University of Technology Sydney（悉尼科技大学）；Centre for Autonomous Systems（自主系统中心）；Centre for Artificial Intelligence（人工智能中心）
This paper presents an observer-integrated Reinforcement Learning (RL) approach, called Disturbance OBserver Network (DOB-Net), for robots operating in environments where disturbances are unknown and time-varying, and may frequently exceed robot control capabilities. The DOB-Net integrates a disturbance dynamics observer network and a controller network. Originated from conventional DOB mechanisms, the observer is built and enhanced via Recurrent Neural Networks (RNNs), encoding estimation of past values and prediction of future values of unknown disturbances in RNN hidden state. Such encoding…
Data-fused MPC with Guarantees: Application to Flying Humanoid Robots
Artificial and Mechanical Intelligence (AMI), Istituto Italiano di Tecnologia (IIT)（人工与机械智能（AMI），意大利技术研究院（IIT））；Robotics, Intelligent Systems and Control, KAUST（机器人、智能系统与控制，王国立阿联酋科学技术大学（KAUST））
A Safe Reinforcement Learning driven Weights-varying Model Predictive Control for Autonomous Vehicle Motion Control
Technical University Munich（慕尼黑工业大学）；TUM School of Engineering and Design（慕尼黑工业大学工程与设计学院）；Munich Institute of Robotics and Machine Intelligence (MIRMI)（慕尼黑机器人与机器智能研究所）
We design an model predictive control (MPC) approach for planning and control of non-holonomic mobile robots. Linearizing the system dynamics around the pre-computed reference trajectory gives a time-varying LQ MPC problem. We analytically show that by specially designing the MPC controller, the time-varying, linearized system can yield asymptotic stability around the origin in the tracking task. We further propose two obstacle avoidance methods. We show that by defining linearized constraint in velocity-space and explicitly coupling the two control inputs based on current state, our second me…
TransMPC: Transformer-based Explicit MPC with Variable Prediction Horizon
School of Mechanical Engineering, University of Science and Technology Beijing（北京科技大学机械工程学院）；School of Mechanical Engineering, Beijing Institute of Technology（北京理工大学机械工程学院）；School of Mechanical Engineering, Nanjing University of Industry Technology（南京工业技术大学机械工程学院）
Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM), CNRS–University of Montpellier（蒙彼利埃计算机科学、机器人技术与微电子实验室（LIRMM），法国国家科学研究中心–蒙彼利埃大学）；School of Mechanical and Aerospace Engineering, Nanyang Technological University（南洋理工大学机械与航空航天工程学院）
We present a model predictive controller (MPC) for multi-contact locomotion where predictive optimizations are realized by time-optimal path parameterization (TOPP). A key feature of this solution is that, contrary to existing planners where step timings are provided as inputs, here the timing between contact switches is computed as output of a fast nonlinear optimization. This is particularly appealing to multi-contact locomotion, where proper timings depend on terrain topology and suitable heuristics are unknown. We show how to formulate legged locomotion as a TOPP problem and demonstrate th…
Agile quadrotor flight in challenging environments has the potential to revolutionize shipping, transportation, and search and rescue applications. Nonlinear model predictive control (NMPC) has recently shown promising results for agile quadrotor control, but relies on highly accurate models for maximum performance. Hence, model uncertainties in the form of unmodeled complex aerodynamic effects, varying payloads and parameter mismatch will degrade overall system performance. In this paper, we propose L1-NMPC, a novel hybrid adaptive NMPC to learn model uncertainties online and immediately comp…
Legged robots have shown remarkable advantages in navigating uneven terrain. However, realizing effective locomotion and manipulation tasks on quadruped robots is still challenging. In addition, object and terrain parameters are generally unknown to the robot in these problems. Therefore, this paper proposes a hierarchical adaptive control framework that enables legged robots to perform loco-manipulation tasks without any given assumption on the object's mass, the friction coefficient, or the slope of the terrain. In our approach, we first present an adaptive manipulation control to regulate t…
University of Toronto Institute for Aerospace Studies（多伦多大学航空航天研究所）
We present a control method for improved repetitive path following for a ground vehicle that is geared towards long-term operation where the operating conditions can change over time and are initially unknown. We use weighted Bayesian Linear Regression (wBLR) to model the unknown dynamics, and show how this simple model is more accurate in both its estimate of the mean behaviour and model uncertainty than Gaussian Process Regression and generalizes to novel operating conditions with little or no tuning. In addition, wBLR allows us to use fast adaptation and long-term learning in one, unified f…
A Task Decomposition method for iterative learning Model Predictive Control (TDMPC) for linear time-varying systems is presented. We consider the availability of state-input trajectories which solve an original task T1, and design a feasible MPC policy for a new task, T2, using stored data from T1. Our approach applies to tasks T2 which are composed of subtasks contained in T1. In this paper we formally define the task decomposition problem, and provide a feasibility proof for the resulting policy. The proposed algorithm reduces the computational burden for linear time-varying systems with pie…
Gaussian Process (GP) regressions have proven to be a valuable tool to predict disturbances and model mismatches and incorporate this information into a Model Predictive Control (MPC) prediction. Unfortunately, the computational complexity of inference and learning on classical GPs scales cubically, which is intractable for real-time applications. Thus GPs are commonly trained offline, which is not suited for learning disturbances as their dynamics may vary with time. Recently, state-space formulation of GPs has been introduced, allowing inference and learning with linear computational complex…
Rollout approaches are an effective tool to address the problem of co-designing the transmission schedule and the corresponding input values, when the controller is connected to the plant via a resource-constrained communication network. These approaches typically employ an MPC, activated at multiples of the period length of a base transmission schedule. Using multi-step invariant terminal regions and a prediction horizon longer than the base period, stability can be ensured. This strategy, however, suffers from intrinsic shortcomings, such as a high computational complexity and low robustness…
We present differentiable predictive control (DPC) as a deep learning-based alternative to the explicit model predictive control (MPC) for unknown nonlinear systems. In the DPC framework, a neural state-space model is learned from time-series measurements of the system dynamics. The neural control policy is then optimized via stochastic gradient descent approach by differentiating the MPC loss function through the closed-loop system dynamics model. The proposed DPC method learns model-based control policies with state and input constraints, while supporting time-varying references and constrai…
T2S-MPC: Time-Embedded Online Adaptive Model Predictive Control for Time-Varying Dynamics
JHU Department of Applied Mathematics and Statistics, Johns Hopkins University, MD, USA（约翰霍普金斯大学应用数学与统计学系）；CMU Department of Electrical and Computer Engineering, Carnegie Mellon University, PA, USA（卡内基梅隆大学电气与计算机工程系）
In this paper, we address the stochastic MPC (SMPC) problem for linear systems, subject to chance state constraints and hard input constraints, under unknown noise distribution. First, we reformulate the chance state constraints as deterministic constraints depending only on explicit noise statistics. Based on these reformulated constraints, we design a distributionally robust and robustly stable benchmark SMPC algorithm for the ideal setting of known noise statistics. Then, we employ this benchmark controller to derive a novel robustly stable adaptive SMPC scheme that learns the necessary noi…
In this paper we are interested in the problem of adaptive state observation of linear time-varying (LTV) systems where the system and the input matrices depend on unknown time-varying parameters. It is assumed that these parameters satisfy some known LTV dynamics, but with unknown initial conditions. Moreover, the state equation is perturbed by an additive signal generated from an exosystem with uncertain constant parameters. Our main contribution is to propose a globally convergent state observer that requires only a weak excitation assumption on the system.
Adaptive Data-Driven Min-Max MPC for Linear Time-Varying Systems
University of Stuttgart（斯图加特大学）；Institute for Systems Theory and Automatic Control, University of Stuttgart（斯图加特大学系统理论与自动控制研究所）；Center for Integrated Quantum Science and Technology (IQST), University of Stuttgart（斯图加特大学集成量子科学与技术中心）
This paper deals with the problem of formulating an adaptive Model Predictive Control strategy for constrained uncertain systems. We consider a linear system, in presence of bounded time varying additive uncertainty. The uncertainty is decoupled as the sum of a process noise with known bounds, and a time varying offset that we wish to identify. The time varying offset uncertainty is assumed unknown point-wise in time. Its domain, called the Feasible Parameter Set, and its maximum rate of change are known to the control designer. As new data becomes available, we refine the Feasible Parameter S…
We present a learning model predictive control (MPC) scheme for chance-constrained Markov jump systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show that…
Gaussian Process Model Predictive Control of Unknown Nonlinear Systems
School of Engineering and Advanced Technology, Massey University（梅西大学工程与先进技术学院）；Department of Information Technology and Software Engineering, Auckland University of Technology（奥克兰理工大学信息技术与软件工程系）
National University of Defense Technology（国防科技大学）；Jilin University（吉林大学）
Robust model predictive control (MPC) is a well-known control technique for model-based control with constraints and uncertainties. In classic robust tube-based MPC approaches, an open-loop control sequence is computed via periodically solving an online nominal MPC problem, which requires prior model information and frequent access to onboard computational resources. In this paper, we propose an efficient robust MPC solution based on receding horizon reinforcement learning, called r-LPC, for unknown nonlinear systems with state constraints and disturbances. The proposed r-LPC utilizes a Koopma…
In this paper, we propose a data-driven economic model predictive control (EMPC) scheme with generalized terminal constraint to control an unknown linear time-invariant system. Our scheme is based on the Fundamental Lemma to predict future system trajectories using a persistently exciting input-output trajectory. The control objective is to minimize an economic cost objective. By employing a generalized terminal constraint with artificial equilibrium, the scheme does not require prior knowledge of the optimal equilibrium. We prove that the asymptotic average performance of the closed-loop syst…
We provide a comprehensive review and practical implementation of a recently developed model predictive control (MPC) framework for controlling unknown systems using only measured data and no explicit model knowledge. Our approach relies on an implicit system parametrization from behavioral systems theory based on one measured input-output trajectory. The presented MPC schemes guarantee closed-loop stability for unknown linear time-invariant (LTI) systems, even if the data are affected by noise. Further, we extend this MPC framework to control unknown nonlinear systems by continuously updating…
