We propose a method to encourage safety in Model Predictive Control (MPC)-based Reinforcement Learning (RL) via Gaussian Process (GP) regression. This framework consists of 1) a parametric MPC scheme that is employed as model-based controller with approximate knowledge on the real system's dynamics, 2) an episodic RL algorithm tasked with adjusting the MPC parametrization in order to increase its performance, and lastly, 3) GP regressors used to estimate, directly from data, constraints on the MPC parameters capable of predicting, up to some probability, whether the parametrization is likely to yield a safe or unsafe policy. These constraints are then enforced onto the RL updates in an effort to enhance the learning method with a probabilistic safety mechanism. Compared to other recent publications combining safe RL with MPC, our method does not require further assumptions on, e.g., the prediction model in order to retain computational tractability. We illustrate the results of our method in a numerical example on the control of a quadrotor drone in a safety-critical environment.
Variable-speed pumped-storage (VSPS) has great potential in helping solve the frequency control problem caused by low inertia, owing to its remarkable flexibility beyond conventional fixed-speed one, to make better use of which, a primary frequency control strategy based on adaptive model predictive control (AMPC) is proposed in this paper for VSPS plant in power generation.
A computationally efficient Model-Predictive Control (MPC) approach is proposed for systems with unknown delay using only input/output data. We use the Koopman operator framework and the related Hankel Alternative View of Koopman (HAVOK) algorithm to identify a model in a basis of projected time-delay coordinates and demonstrate a novel MPC structure that reduces and bounds the computational complexity. The proposed HAVOK-MPC approach is validated experimentally on a laboratory-scale District Heating System (DHS), demonstrating excellent prediction and tracking performance while only requiring knowledge of a conservative upper bound on the system delay.
An increase in the integration of Inverter Based Resources (IBRs) to the electric grid, will lead to a corresponding decrease in the amount of connected synchronous generators, resulting in a decline in the available rotational inertia system-wide. This can lead to pronounced frequency deviations when there are disturbances and faults in the grid. This decline in available rotational inertia can be compensated for by fast acting IBRs participating in frequency response services, by rapidly injecting into or removing power from the grid. Currently, there are still relative small number of sizable IBRs in the grid. Therefore, the placement of the IBRs in the system, as well as the inverter configuration type and controller, will have a material impact on the frequency response of the grid. In this work, we present an optimal placement algorithm that maximizes the benefits of utilizing IBRs in providing frequency response services. That is, we minimize the overall system frequency deviation while using a minimal amount of electric power injection from the IBRs. The proposed algorithm uses the resistance distance to place the IBRs at nodes that are central to the rest of the nodes in the network thus minimizing the distance of power flow. The proposed greedy algorithm achieves a near optimal performance and relies on the supermodularity of the resistance distances. We validate the performance of the placement algorithm on three IEEE test systems of varying sizes, by comparing its performance to an exhaustive search algorithm. We further evaluate the performance of the placed IBRs on an IEEE test system, to determine their impact on frequency stability. The IBRs are configured in a grid-forming mode and equipped with a model predictive control (MPC)-based inverter power control.
In this paper, we propose a Risk-Averse Priced Timed Automata (PTA) Model Predictive Control (MPC) framework to increase flexibility of cyber-physical systems. To improve flexibility in these systems, our risk-averse framework solves a multi-objective optimization problem to minimize the cost and risk, simultaneously. While minimizing cost ensures the least effort to achieve a task, minimizing risk provides guarantees on the feasibility of the task even during uncertainty. Our framework explores the trade-off between these two qualities to obtain risk-averse control actions. The solution of risk-averse PTA MPC dynamic decision-making algorithm reacts relatively better to PTA changes compared to PTA MPC without risk-averse feature. An example from manufacturing systems is presented to show the application of the proposed control strategy.
Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in the presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. In this paper, we present a self-supervised learning approach that actively models the dynamics of nonlinear robotic systems. We combine offline learning from past experience and online learning from current robot interaction with the unknown environment. These two ingredients enable a highly sample-efficient and adaptive learning process, capable of accurately inferring model dynamics in real-time even in operating regimes that greatly differ from the training distribution. Moreover, we design an uncertainty-aware model predictive controller that is heuristically conditioned to the aleatoric (data) uncertainty of the learned dynamics. This controller actively chooses the optimal control actions that (i) optimize the control performance and (ii) improve the efficiency of online learning sample collection. We demonstrate the effectiveness of our method through a series of challenging real-world experiments using a quadrotor system. Our approach showcases high resilience and generalization capabilities by consistently adapting to unseen flight conditions, while it significantly outperforms classical and adaptive control baselines.
How much explicit guidance is necessary for conditional diffusion? We consider the problem of conditional sampling using an unconditional diffusion model and limited explicit guidance (e.g., a noised classifier, or a conditional diffusion model) that is restricted to a small number of time steps. We explore a model predictive control (MPC)-like approach to approximate guidance by simulating unconditional diffusion forward, and backpropagating explicit guidance feedback. MPC-approximated guides have high cosine similarity to real guides, even over large simulation distances. Adding MPC steps improves generative quality when explicit guidance is limited to five time steps.
Robotic manipulation stands as a largely unsolved problem despite significant advances in robotics and machine learning in recent years. One of the key challenges in manipulation is the exploration of the dynamics of the environment when there is continuous contact between the objects being manipulated. This paper proposes a model-based active exploration approach that enables efficient learning in sparse-reward robotic manipulation tasks. The proposed method estimates an information gain objective using an ensemble of probabilistic models and deploys model predictive control (MPC) to plan actions online that maximize the expected reward while also performing directed exploration. We evaluate our proposed algorithm in simulation and on a real robot, trained from scratch with our method, on a challenging ball pushing task on tilted tables, where the target ball position is not known to the agent a-priori. Our real-world robot experiment serves as a fundamental application of active exploration in model-based reinforcement learning of complex robotic manipulation tasks.
We present a system for collision-free control of a robot manipulator that uses only RGB views of the world. Perceptual input of a tabletop scene is provided by multiple images of an RGB camera (without depth) that is either handheld or mounted on the robot end effector. A NeRF-like process is used to reconstruct the 3D geometry of the scene, from which the Euclidean full signed distance function (ESDF) is computed. A model predictive control algorithm is then used to control the manipulator to reach a desired pose while avoiding obstacles in the ESDF. We show results on a real dataset collected and annotated in our lab.
Vehicle stability control systems are important components of active safety systems for road transport. The problem of vehicle lateral stability control is addressed in this paper using active front wheel steering and individual braking. Vehicle lateral stability control means keeping the vehicle yaw rate and the vehicle side slip angle in desired values. For this reason, a model-based controller is designed. The desired yaw rate is obtained from the single track vehicle model and the desired side slip angle is chosen as zero. Controller design consists of two parts, lower and upper controller parts. Upper controller is designed based on Model Predictive Control (MPC) method. This upper controller changes front wheel steering angles utilizing steer-by-wire system and also it generates the required control moment for stabilizing the yaw motion of the vehicle. Lower controller is an individual braking algorithm. It determines the individual braking wheel. In this way, the control moment can be applied to the vehicle. The designed controller is tested using the nonlinear single track vehicle model and the higher fidelity CarMaker vehicle model.
We present a sequential distributed model predictive control (MPC) scheme for cooperative control of multi-agent systems with dynamically decoupled heterogeneous nonlinear agents subject to individual constraints. In the scheme, we explore the idea of using tracking MPC with artificial references to let agents coordinate their cooperation without external guidance. Each agent combines a tracking MPC with artificial references, the latter penalized by a suitable coupling cost. They solve an individual optimization problem for this artificial reference and an input that tracks it, only communicating the former to its neighbors in a communication graph. This puts the cooperative problem on a different layer than the handling of the dynamics and constraints, loosening the connection between the two. We provide sufficient conditions on the formulation of the cooperative problem and the coupling cost for the closed-loop system to asymptotically achieve it. Since the dynamics and the cooperative problem are only loosely connected, classical results from distributed optimization can be used to this end. We illustrate the scheme's application to consensus and formation control.
In this paper, we leverage the rapid advances in imitation learning, a topic of intense recent focus in the Reinforcement Learning (RL) literature, to develop new sample complexity results and performance guarantees for data-driven Model Predictive Control (MPC) for constrained linear systems. In its simplest form, imitation learning is an approach that tries to learn an expert policy by querying samples from an expert. Recent approaches to data-driven MPC have used the simplest form of imitation learning known as behavior cloning to learn controllers that mimic the performance of MPC by online sampling of the trajectories of the closed-loop MPC system. Behavior cloning, however, is a method that is known to be data inefficient and suffer from distribution shifts. As an alternative, we develop a variant of the forward training algorithm which is an on-policy imitation learning method proposed by Ross et al. (2010). Our algorithm uses the structure of constrained linear MPC, and our analysis uses the properties of the explicit MPC solution to theoretically bound the number of online MPC trajectories needed to achieve optimal performance. We validate our results through simulations and show that the forward training algorithm is indeed superior to behavior cloning when applied to MPC.
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 complexity. This paper presents a framework that enables online learning of disturbance dynamics on quadcopters, which can be executed within milliseconds using a state-space formulation of GPs. The obtained disturbance predictions are combined with MPC leading to a significant performance increase in simulations with jMAVSim. The computational burden is evaluated on a Raspberry Pi 4 B to prove the real-time applicability.
This paper presents a robust Model Predictive Control (MPC) scheme that provides offset-free setpoint tracking for systems described by Neural Nonlinear AutoRegressive eXogenous (NNARX) models. The NNARX model learns the dynamics of the plant from input-output data, and during the training the Incremental Input-to-State Stability (${\delta}$ISS) property is forced to guarantee stability. The trained NNARX model is then augmented with an explicit integral action on the output tracking error, which allows the control scheme to enjoy offset-free tracking ability. A tube-based MPC is finally designed, leveraging the unique structure of the model, to ensure robust stability and robust asymptotic zero error regulation for constant reference signals in the presence of model-plant mismatch or unknown disturbances. Numerical simulations on a water heating system show the effectiveness of the proposed control algorithm.
This paper shows that the optimal policy and value functions of a Markov Decision Process (MDP), either discounted or not, can be captured by a finite-horizon undiscounted Optimal Control Problem (OCP), even if based on an inexact model. This can be achieved by selecting a proper stage cost and terminal cost for the OCP. A very useful particular case of OCP is a Model Predictive Control (MPC) scheme where a deterministic (possibly nonlinear) model is used to reduce the computational complexity. This observation leads us to parameterize an MPC scheme fully, including the cost function. In practice, Reinforcement Learning algorithms can then be used to tune the parameterized MPC scheme. We verify the developed theorems analytically in an LQR case and we investigate some other nonlinear examples in simulations.
Monte Carlo methods have become increasingly relevant for control of non-differentiable systems, approximate dynamics models and learning from data. These methods scale to high-dimensional spaces and are effective at the non-convex optimizations often seen in robot learning. We look at sample-based methods from the perspective of inference-based control, specifically posterior policy iteration. From this perspective, we highlight how Gaussian noise priors produce rough control actions that are unsuitable for physical robot deployment. Considering smoother Gaussian process priors, as used in episodic reinforcement learning and motion planning, we demonstrate how smoother model predictive control can be achieved using online sequential inference. This inference is realized through an efficient factorization of the action distribution and a novel means of optimizing the likelihood temperature to improve importance sampling accuracy. We evaluate this approach on several high-dimensional robot control tasks, matching the sample efficiency of prior heuristic methods while also ensuring smoothness. Simulation results can be seen at https://monte-carlo-ppi.github.io/.
This paper proposes a control architecture for autonomous lane keeping by a vehicle. In this paper, the vehicle dynamics consist of two parts: lateral and longitudinal dynamics. Therefore, the control architecture comprises two subsequent controllers. A longitudinal model predictive control (MPC) makes the vehicle track the desired longitudinal speeds that are assumed to be generated by a speed planner. The longitudinal speeds are then passed to a lateral MPC for lane keeping. Due to the dependence of the lateral dynamics on the longitudinal speed, they are represented in a linear parameter-varying (LPV) form, where its scheduling parameter is the longitudinal speed of the vehicle. In order to deal with the imprecise information of the future longitudinal speed (the scheduling parameter), a bound of uncertainty is considered around the nominal trajectory of the future longitudinal velocities. Then, a tube-based LPV- MPC is adopted to control the lateral dynamics for attaining the lane keeping goal. In the end, the effectiveness of the proposed methods is illustrated by carrying out simulation tests.
Electric-powered wheelchair plays an important role in providing accessibility for people with mobility impairment. Ensuring the safety of wheelchair operation in different application scenarios and for diverse users is crucial when the designing controller for tracking tasks. In this work, we propose a safety-based speed tracking control algorithm for wheelchair systems with external disturbances and uncertain parameters at the dynamic level. The set-membership approach is applied to estimate the sets of uncertain parameters online and a designed model predictive control scheme with online model and control parameter adaptation is presented to guarantee safety-related constraints during the tracking process. The proposed controller can drive the wheelchair speed to a desired reference within safety constraints. For the inadmissible reference that violates the constraints, the proposed controller can steer the system to the neighbourhood of the closest admissible reference. The effectiveness of the proposed control scheme is validated based on the high-fidelity speed tracking results of two tasks that involve feasible and infeasible references.
Data-driven controls using Gaussian process regression have recently gained much attention. In such approaches, system identification by Gaussian process regression is mostly followed by model-based controller designs. However, the outcomes of Gaussian process regression are often too complicated to apply conventional control designs, which makes the numerical design such as model predictive control employed in many cases. To overcome the restriction, our idea is to perform Gaussian process regression to the inverse of the plant with the same input/output data for the conventional regression. With the inverse, one can design a model reference controller without resorting to numerical control methods. This paper considers single-input single-output (SISO) discrete-time nonlinear systems of minimum phase with relative degree one. It is highlighted that the model reference Gaussian process regression controller is designed directly from pre-collected input/output data without system identification.
Reinforcement learning (RL) has recently proven great success in various domains. Yet, the design of the reward function requires detailed domain expertise and tedious fine-tuning to ensure that agents are able to learn the desired behaviour. Using a sparse reward conveniently mitigates these challenges. However, the sparse reward represents a challenge on its own, often resulting in unsuccessful training of the agent. In this paper, we therefore address the sparse reward problem in RL. Our goal is to find an effective alternative to reward shaping, without using costly human demonstrations, that would also be applicable to a wide range of domains. Hence, we propose to use model predictive control~(MPC) as an experience source for training RL agents in sparse reward environments. Without the need for reward shaping, we successfully apply our approach in the field of mobile robot navigation both in simulation and real-world experiments with a Kuboki Turtlebot 2. We furthermore demonstrate great improvement over pure RL algorithms in terms of success rate as well as number of collisions and timeouts. Our experiments show that MPC as an experience source improves the agent's learning process for a given task in the case of sparse rewards.