Publications
1.
Zhang, Shuhao; Swevers, Jan
Time-optimal Point-to-point Motion Planning: A Two-stage Approach Proceedings Article Forthcoming
In: Forthcoming, (Accepted to the 2024 IFAC Conference on Nonlinear Model Predictive Control (NMPC)).
@inproceedings{Zhang2024TimeOpt,
title = {Time-optimal Point-to-point Motion Planning: A Two-stage Approach},
author = {Shuhao Zhang and Jan Swevers},
url = {https://doi.org/10.48550/arXiv.2403.03573},
year = {2024},
date = {2024-04-16},
abstract = {This paper proposes a two-stage approach to formulate the time-optimal point-to-point motion planning problem, involving a first stage with a fixed time grid and a second stage with a variable time grid. The proposed approach brings benefits through its straightforward optimal control problem formulation with a fixed and low number of control steps for manageable computational complexity and the avoidance of interpolation errors associated with time scaling, especially when aiming to reach a distant goal. Additionally, an asynchronous nonlinear model predictive control (NMPC) update scheme is integrated with this two-stage approach to address delayed and fluctuating computation times, facilitating online replanning. The effectiveness of the proposed two-stage approach and NMPC implementation is demonstrated through numerical examples centered on autonomous navigation with collision avoidance.},
note = {Accepted to the 2024 IFAC Conference on Nonlinear Model Predictive Control (NMPC)},
keywords = {},
pubstate = {forthcoming},
tppubtype = {inproceedings}
}
This paper proposes a two-stage approach to formulate the time-optimal point-to-point motion planning problem, involving a first stage with a fixed time grid and a second stage with a variable time grid. The proposed approach brings benefits through its straightforward optimal control problem formulation with a fixed and low number of control steps for manageable computational complexity and the avoidance of interpolation errors associated with time scaling, especially when aiming to reach a distant goal. Additionally, an asynchronous nonlinear model predictive control (NMPC) update scheme is integrated with this two-stage approach to address delayed and fluctuating computation times, facilitating online replanning. The effectiveness of the proposed two-stage approach and NMPC implementation is demonstrated through numerical examples centered on autonomous navigation with collision avoidance.
2.
Løwenstein, Kristoffer Fink; Fagiano, Lorenzo; Bernardini, Daniele; Bemporad, Alberto
Physics-Informed Online Learning by Moving Horizon Estimation: Learning Recurrent Neural Networks in Gray-box Models Proceedings Forthcoming
Forthcoming, (Accepted to the 2024 IFAC Conference on Nonlinear Model Predictive Control (NMPC)).
@proceedings{Lowenstein2024PhysicsInformedRNN,
title = {Physics-Informed Online Learning by Moving Horizon Estimation: Learning Recurrent Neural Networks in Gray-box Models},
author = {Kristoffer Fink Løwenstein and Lorenzo Fagiano and Daniele Bernardini and Alberto Bemporad},
year = {2024},
date = {2024-04-02},
abstract = {In Model Predictive Control (MPC) closed-loop performance heavily depends on the quality of the underlying prediction model, where such a model must be accurate and yet
simple. A key feature in modern MPC applications is the potential for online model adaptation to cope with time-varying changes, part-to-part variations, and complex features of the system dynamics not caught by models derived from first principles. In this paper, we propose to use a physics-informed, or gray-box, model that extends the physics-based model with a data-driven component, namely a Recurrent Neural Network (RNN). Relying on physics-informed models allows for a rather limited size of the RNN, thereby enhancing online applicability compared to pure black-box models. This work presents a method based on Moving Horizon Estimation (MHE) for simultaneous state estimation and learning of the RNN sub-model, a potentially challenging issue due to limited information available in noisy input output data and lack of knowledge of the internal state of the RNN. We provide a case study on a quadruple tank benchmark showing how the method can cope with part-to-part variations.},
note = {Accepted to the 2024 IFAC Conference on Nonlinear Model Predictive Control (NMPC)},
keywords = {},
pubstate = {forthcoming},
tppubtype = {proceedings}
}
In Model Predictive Control (MPC) closed-loop performance heavily depends on the quality of the underlying prediction model, where such a model must be accurate and yet
simple. A key feature in modern MPC applications is the potential for online model adaptation to cope with time-varying changes, part-to-part variations, and complex features of the system dynamics not caught by models derived from first principles. In this paper, we propose to use a physics-informed, or gray-box, model that extends the physics-based model with a data-driven component, namely a Recurrent Neural Network (RNN). Relying on physics-informed models allows for a rather limited size of the RNN, thereby enhancing online applicability compared to pure black-box models. This work presents a method based on Moving Horizon Estimation (MHE) for simultaneous state estimation and learning of the RNN sub-model, a potentially challenging issue due to limited information available in noisy input output data and lack of knowledge of the internal state of the RNN. We provide a case study on a quadruple tank benchmark showing how the method can cope with part-to-part variations.
simple. A key feature in modern MPC applications is the potential for online model adaptation to cope with time-varying changes, part-to-part variations, and complex features of the system dynamics not caught by models derived from first principles. In this paper, we propose to use a physics-informed, or gray-box, model that extends the physics-based model with a data-driven component, namely a Recurrent Neural Network (RNN). Relying on physics-informed models allows for a rather limited size of the RNN, thereby enhancing online applicability compared to pure black-box models. This work presents a method based on Moving Horizon Estimation (MHE) for simultaneous state estimation and learning of the RNN sub-model, a potentially challenging issue due to limited information available in noisy input output data and lack of knowledge of the internal state of the RNN. We provide a case study on a quadruple tank benchmark showing how the method can cope with part-to-part variations.
3.
Meza, Gonzalo; Løwenstein, Kristoffer Fink; Fagiano, Lorenzo
Obstacle avoidance for a robotic manipulator with linear-quadratic Model Predictive Control Working paper
2024, (Submitted to the 2024 IEEE 20th International Conference on Automation Science and Engineering (CASE 2024)).
@workingpaper{Meza2024ObstacleMPC,
title = {Obstacle avoidance for a robotic manipulator with linear-quadratic Model Predictive Control},
author = {Gonzalo Meza and Kristoffer Fink Løwenstein and Lorenzo Fagiano },
year = {2024},
date = {2024-04-02},
urldate = {2024-04-02},
abstract = {The problem of moving a six-degrees-of-freedom manipulator in an environment with unknown obstacles is considered. The manipulator is assumed to be equipped with an exteroceptive sensor that provides a partial sampling of the surroundings. A hierarchical control layout is proposed: in the outer layer, a path planner generates an obstacle free trajectory based on the available local information; in the inner layer, a Model-Predictive Controller formulated in the joint space tracks the trajectory while reactively avoiding unseen obstacles at a higher rate. By constructing a polytopic under-approximation of the free environment end employing a suitable estimate of the Jacobian matrix of the manipulator, the predictive controller features a convex quadratic cost and linear constraints, thus requiring the solution of a quadratic program at each time step. The proposed method is evaluated on the kinematic model of a MyCobot280 robotic arm, showing the potential for real-time feasibility.},
note = {Submitted to the 2024 IEEE 20th International Conference on Automation Science and Engineering (CASE 2024)},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
The problem of moving a six-degrees-of-freedom manipulator in an environment with unknown obstacles is considered. The manipulator is assumed to be equipped with an exteroceptive sensor that provides a partial sampling of the surroundings. A hierarchical control layout is proposed: in the outer layer, a path planner generates an obstacle free trajectory based on the available local information; in the inner layer, a Model-Predictive Controller formulated in the joint space tracks the trajectory while reactively avoiding unseen obstacles at a higher rate. By constructing a polytopic under-approximation of the free environment end employing a suitable estimate of the Jacobian matrix of the manipulator, the predictive controller features a convex quadratic cost and linear constraints, thus requiring the solution of a quadratic program at each time step. The proposed method is evaluated on the kinematic model of a MyCobot280 robotic arm, showing the potential for real-time feasibility.
4.
Løwenstein, Kristoffer Fink; Bernardini, Daniele; Patrinos, Panagiotis
QPALM-OCP: A Newton-type Proximal Augmented Lagrangian tailored for Quadratic Programs arising in Model Predictive Control Working paper
2024, (Submitted to the 63rd IEEE Conference on Decision and Control 2024 (CDC)).
@workingpaper{Lowenstein2024QPALMOCP,
title = {QPALM-OCP: A Newton-type Proximal Augmented Lagrangian tailored for Quadratic Programs arising in Model Predictive Control},
author = {Kristoffer Fink Løwenstein and Daniele Bernardini and Panagiotis Patrinos},
year = {2024},
date = {2024-04-02},
abstract = {In Model Predictive Control (MPC) fast and reliable Quadratic Programming (QP) solvers are of fundamental importance. The inherent structure of the subsequent Optimal Control Problems (OCPs) can lead to substantial performance improvements if exploited. Therefore, we present a structure-exploiting proximal augmented Lagrangian based solver extending the general-purpose QP-solver QPALM. Our solver relies on semismooth Newton iterates to solve the inner sub-problem while directly accounting for the OCP structure via efficient and sparse matrix factorizations. The matrices to be factorized depends on the active set and therefore low-rank factorization updates can be employed like in active-set methods resulting in cheap iterates. We benchmark our solver against other state-of-the-art QP-solvers and our algorithm compare favorably against these solvers},
note = {Submitted to the 63rd IEEE Conference on Decision and Control 2024 (CDC)},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
In Model Predictive Control (MPC) fast and reliable Quadratic Programming (QP) solvers are of fundamental importance. The inherent structure of the subsequent Optimal Control Problems (OCPs) can lead to substantial performance improvements if exploited. Therefore, we present a structure-exploiting proximal augmented Lagrangian based solver extending the general-purpose QP-solver QPALM. Our solver relies on semismooth Newton iterates to solve the inner sub-problem while directly accounting for the OCP structure via efficient and sparse matrix factorizations. The matrices to be factorized depends on the active set and therefore low-rank factorization updates can be employed like in active-set methods resulting in cheap iterates. We benchmark our solver against other state-of-the-art QP-solvers and our algorithm compare favorably against these solvers
5.
Messerer, Florian; Baumgärtner, Katrin; Lucia, Sergio; Diehl, Moritz
Fourth-order suboptimality of nominal model predictive control in the presence of uncertainty Working paper
2024.
@workingpaper{messerer2024fourthorder,
title = {Fourth-order suboptimality of nominal model predictive control in the presence of uncertainty},
author = {Florian Messerer and Katrin Baumgärtner and Sergio Lucia and Moritz Diehl},
url = {https://arxiv.org/abs/2403.04559},
year = {2024},
date = {2024-03-08},
abstract = {We investigate the suboptimality resulting from the application of nominal model predictive control (MPC) to a nonlinear discrete time stochastic system. The suboptimality is defined with respect to the corresponding stochastic optimal control problem (OCP) that minimizes the expected cost of the closed loop system. In this context, nominal MPC corresponds to a form of certainty-equivalent control (CEC). We prove that, in a smooth and unconstrained setting, the suboptimality growth is of fourth order with respect to the level of uncertainty, a parameter which we can think of as a standard deviation. This implies that the suboptimality does not grow very quickly as the level of uncertainty is increased, providing further insight into the practical success of nominal MPC. Similarly, the difference between the optimal and suboptimal control inputs is of second order. We illustrate the result on a simple numerical example, which we also use to show how the proven relationship may cease to hold in the presence of state constraints.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
We investigate the suboptimality resulting from the application of nominal model predictive control (MPC) to a nonlinear discrete time stochastic system. The suboptimality is defined with respect to the corresponding stochastic optimal control problem (OCP) that minimizes the expected cost of the closed loop system. In this context, nominal MPC corresponds to a form of certainty-equivalent control (CEC). We prove that, in a smooth and unconstrained setting, the suboptimality growth is of fourth order with respect to the level of uncertainty, a parameter which we can think of as a standard deviation. This implies that the suboptimality does not grow very quickly as the level of uncertainty is increased, providing further insight into the practical success of nominal MPC. Similarly, the difference between the optimal and suboptimal control inputs is of second order. We illustrate the result on a simple numerical example, which we also use to show how the proven relationship may cease to hold in the presence of state constraints.
6.
Xie, Jing; Simpson, Léo; Asprion, Jonas; Scattolini, Riccardo
A Learning-based Model Predictive Control Scheme with Application to Temperature Control Units Working paper
2024, (Submitted to 2024 IEEE Conference on Control Technology and Applications).
@workingpaper{xie2024learningbased,
title = {A Learning-based Model Predictive Control Scheme with Application to Temperature Control Units},
author = {Jing Xie and Léo Simpson and Jonas Asprion and Riccardo Scattolini
},
url = {https://arxiv.org/abs/2402.05606},
year = {2024},
date = {2024-02-13},
urldate = {2024-02-13},
abstract = {Temperature control is a complex task due to its often unknown dynamics and disturbances. This paper explores the use of Neural Nonlinear AutoRegressive eXogenous (NNARX) models for nonlinear system identification and model predictive control of a temperature control unit. First, the NNARX model is identified from input-output data collected from the real plant, and a state-space representation with known measurable states consisting of past input and output variables is formulated. Second, a tailored model predictive controller is designed based on the trained NNARX network. The proposed control architecture is experimentally tested on the temperature control units manufactured by Tool-Temp AG. The results achieved are compared with those obtained using a PI controller and a linear MPC. The findings illustrate that the proposed scheme achieves satisfactory tracking performance while incurring the lowest energy cost among the compared controllers.},
note = {Submitted to 2024 IEEE Conference on Control Technology and Applications},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Temperature control is a complex task due to its often unknown dynamics and disturbances. This paper explores the use of Neural Nonlinear AutoRegressive eXogenous (NNARX) models for nonlinear system identification and model predictive control of a temperature control unit. First, the NNARX model is identified from input-output data collected from the real plant, and a state-space representation with known measurable states consisting of past input and output variables is formulated. Second, a tailored model predictive controller is designed based on the trained NNARX network. The proposed control architecture is experimentally tested on the temperature control units manufactured by Tool-Temp AG. The results achieved are compared with those obtained using a PI controller and a linear MPC. The findings illustrate that the proposed scheme achieves satisfactory tracking performance while incurring the lowest energy cost among the compared controllers.
7.
Xie, Jing; Bonassi, Fabio; Scattolini, Riccardo
Internal Model Control design for systems learned by Control Affine Neural Nonlinear Autoregressive Exogenous Models Working paper
2024, (Submitted to IEEE Transactions on Automation Science and Engineering).
@workingpaper{xie2024internal,
title = {Internal Model Control design for systems learned by Control Affine Neural Nonlinear Autoregressive Exogenous Models},
author = {Jing Xie and Fabio Bonassi and Riccardo Scattolini},
url = {https://arxiv.org/abs/2402.05607},
year = {2024},
date = {2024-02-13},
urldate = {2024-02-13},
abstract = {This paper explores the use of Control Affine Neural Nonlinear AutoRegressive eXogenous (CA-NNARX) models for nonlinear system identification and model-based control design. The idea behind this architecture is to match the known control-affine structure of the system to achieve improved performance. Coherently with recent literature of neural networks for data-driven control, we first analyze the stability properties of CA-NNARX models, devising sufficient conditions for their incremental Input-to-State Stability (incremental ISS) that can be enforced at the model training stage. The model's stability property is then leveraged to design a stable Internal Model Control (IMC) architecture. The proposed control scheme is tested on a simulated Quadruple Tank benchmark system to address the output reference tracking problem. The results achieved show that (i) the modeling accuracy of CA-NNARX is superior to the one of a standard NNARX model for given weight size and training epochs, and (ii) the proposed IMC law provides performance comparable to the ones of a standard Model Predictive Controller (MPC) at a significantly lower computational burden.},
note = {Submitted to IEEE Transactions on Automation Science and Engineering},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
This paper explores the use of Control Affine Neural Nonlinear AutoRegressive eXogenous (CA-NNARX) models for nonlinear system identification and model-based control design. The idea behind this architecture is to match the known control-affine structure of the system to achieve improved performance. Coherently with recent literature of neural networks for data-driven control, we first analyze the stability properties of CA-NNARX models, devising sufficient conditions for their incremental Input-to-State Stability (incremental ISS) that can be enforced at the model training stage. The model's stability property is then leveraged to design a stable Internal Model Control (IMC) architecture. The proposed control scheme is tested on a simulated Quadruple Tank benchmark system to address the output reference tracking problem. The results achieved show that (i) the modeling accuracy of CA-NNARX is superior to the one of a standard NNARX model for given weight size and training epochs, and (ii) the proposed IMC law provides performance comparable to the ones of a standard Model Predictive Controller (MPC) at a significantly lower computational burden.
8.
Cecchin, Leonardo; Trachte, Adrian; Fagiano, Lorenzo; Diehl, Moritz
Real-time prediction of human-generated reference signals: a case study in advanced digging control Working paper
2024, (Submitted to the 2024 European Control Conference (ECC)).
@workingpaper{cecchin2024pred,
title = {Real-time prediction of human-generated reference signals: a case study in advanced digging control},
author = {Leonardo Cecchin and Adrian Trachte and Lorenzo Fagiano and Moritz Diehl},
year = {2024},
date = {2024-02-12},
urldate = {2024-02-12},
abstract = {Techniques like Model Predictive Control (MPC) and two-degrees-of-freedom structures (feedforward plus feedback) can improve the control performance by exploiting a prediction of the reference trajectory, which is assumed to be available. This assumption holds true when pre-defined reference trajectories are known a-priori, e.g. constant or piecewise linear, but fails in applications where a human operator chooses the reference at runtime. To cope with this problem, we study different approaches to use the collected data of human-generated reference signals to learn a predictive model of the operator commands. The considered methods are function approximation techniques based on Kriging, Set-Membership, and LSTM Neural Networks.
We summarize the principles and the implementation of each method, and compare their performance using an experimental data-set of operations from a real-world excavator, where four operator-defined reference signals are predicted.},
note = {Submitted to the 2024 European Control Conference (ECC)},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Techniques like Model Predictive Control (MPC) and two-degrees-of-freedom structures (feedforward plus feedback) can improve the control performance by exploiting a prediction of the reference trajectory, which is assumed to be available. This assumption holds true when pre-defined reference trajectories are known a-priori, e.g. constant or piecewise linear, but fails in applications where a human operator chooses the reference at runtime. To cope with this problem, we study different approaches to use the collected data of human-generated reference signals to learn a predictive model of the operator commands. The considered methods are function approximation techniques based on Kriging, Set-Membership, and LSTM Neural Networks.
We summarize the principles and the implementation of each method, and compare their performance using an experimental data-set of operations from a real-world excavator, where four operator-defined reference signals are predicted.
We summarize the principles and the implementation of each method, and compare their performance using an experimental data-set of operations from a real-world excavator, where four operator-defined reference signals are predicted.
9.
Cecchin, Leonardo; Ohtsuka, Toshiyuki; Trachte, Adrian; Diehl, Moritz
Model Predictive Controller for Hydraulic Cylinders with Independent Metering Control Valves Working paper
2024, (Submitted to the 2024 IFAC Conference on Nonlinear Model Predictive Control (NMPC)).
@workingpaper{cecchin2024imc,
title = {Model Predictive Controller for Hydraulic Cylinders with Independent Metering Control Valves},
author = {Leonardo Cecchin and Toshiyuki Ohtsuka and Adrian Trachte and Moritz Diehl},
year = {2024},
date = {2024-02-12},
urldate = {2024-02-12},
abstract = {Hydraulic cylinders are pivotal components in various industrial, construction, and off-highway applications, where efficient actuation is crucial for reducing energy consumption, minimizing heat generation, and extending components' lifespan. The integration of Independent Metering Control, a valve topology allowing five valves to independently control the flow, represents a significant advancement in enhancing hydraulic systems' performance. However, the lack of a reliable and flexible control solution remains a challenge. In this paper, we present the implementation of nonlinear Model Predictive Control, using a favorable model formulation and a state-of-the-art solver. We show how it can deliver close-to-optimal performance with real-time capabilities, addressing the current gap in achieving efficient control for hydraulic cylinders with Independent Metering Control.},
note = {Submitted to the 2024 IFAC Conference on Nonlinear Model Predictive Control (NMPC)},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Hydraulic cylinders are pivotal components in various industrial, construction, and off-highway applications, where efficient actuation is crucial for reducing energy consumption, minimizing heat generation, and extending components' lifespan. The integration of Independent Metering Control, a valve topology allowing five valves to independently control the flow, represents a significant advancement in enhancing hydraulic systems' performance. However, the lack of a reliable and flexible control solution remains a challenge. In this paper, we present the implementation of nonlinear Model Predictive Control, using a favorable model formulation and a state-of-the-art solver. We show how it can deliver close-to-optimal performance with real-time capabilities, addressing the current gap in achieving efficient control for hydraulic cylinders with Independent Metering Control.
10.
Zhang, Shuhao; Bos, Mathis; Vandewal, Bastiaan; Decré, Wilm; Gillis, Joris; Swevers, Jan
Robustified Time-optimal Collision-free Motion Planning for Autonomous Mobile Robots under Disturbance Conditions Working paper Forthcoming
Forthcoming, (Accepted to be presented at the 2024 IEEE International Conference on Robotics and Automation (ICRA)).
@workingpaper{lirias4141698,
title = {Robustified Time-optimal Collision-free Motion Planning for Autonomous Mobile Robots under Disturbance Conditions},
author = {Shuhao Zhang and Mathis Bos and Bastiaan Vandewal and Wilm Decré and Joris Gillis and Jan Swevers},
url = {https://kuleuven.limo.libis.be/discovery/fulldisplay?docid=lirias4141698&context=SearchWebhook&vid=32KUL_KUL:Lirias&search_scope=lirias_profile&adaptor=SearchWebhook&tab=LIRIAS&query=any,contains,LIRIAS4141698&offset=0},
year = {2024},
date = {2024-02-07},
urldate = {2024-02-07},
abstract = {This paper presents a robustified time-optimal motion planning approach for navigating an Autonomous Mobile Robot (AMR) from an initial state to a terminal state without colliding with obstacles and while affected by disturbances modeled as random process and measurement noise. The approach iteratively solves the robustified problem by incorporating updated state-dependent safety margins for collision avoidance, the evolution of which is derived separately from the robustified problem. Additionally, a strategy for selecting an alternative terminal state to reach is introduced, which comes into play when the desired terminal state becomes infeasible considering the uncertainties. Both of these contributions are integrated into a robustified motion planning and control pipeline, the efficacy of which is validated through simulation experiments.},
note = {Accepted to be presented at the 2024 IEEE International Conference on Robotics and Automation (ICRA)},
keywords = {},
pubstate = {forthcoming},
tppubtype = {workingpaper}
}
This paper presents a robustified time-optimal motion planning approach for navigating an Autonomous Mobile Robot (AMR) from an initial state to a terminal state without colliding with obstacles and while affected by disturbances modeled as random process and measurement noise. The approach iteratively solves the robustified problem by incorporating updated state-dependent safety margins for collision avoidance, the evolution of which is derived separately from the robustified problem. Additionally, a strategy for selecting an alternative terminal state to reach is introduced, which comes into play when the desired terminal state becomes infeasible considering the uncertainties. Both of these contributions are integrated into a robustified motion planning and control pipeline, the efficacy of which is validated through simulation experiments.
11.
Zhang, Shuhao; Swevers, Jan
Two-stage Time-optimal Motion Planning Presentation
07.02.2024, (Abstract at the 2024 Benelux Meeting ).
@misc{lirias4141067,
title = {Two-stage Time-optimal Motion Planning},
author = {Shuhao Zhang and Jan Swevers},
year = {2024},
date = {2024-02-07},
urldate = {2024-02-07},
note = {Abstract at the 2024 Benelux Meeting },
keywords = {},
pubstate = {published},
tppubtype = {presentation}
}
12.
Lahr, Amon; Tronarp, Filip; Schmidt, Nathanael Bosch Jonathan; Hennig, Philipp; Zeilinger, Melanie N.
Probabilistic ODE Solvers for Integration Error-Aware Model Predictive Control Working paper
2024, (Submitted to the 6th Annual Learning for Dynamics & Control Conference (L4DC 2024)).
@workingpaper{lahr_probabilistic_2024,
title = {Probabilistic ODE Solvers for Integration Error-Aware Model Predictive Control},
author = {Amon Lahr and Filip Tronarp and Nathanael Bosch Jonathan Schmidt and Philipp Hennig and Melanie N. Zeilinger},
url = {https://doi.org/10.48550/arXiv.2401.17731},
year = {2024},
date = {2024-02-07},
urldate = {2024-02-07},
abstract = {Appropriate time discretization is crucial for nonlinear model predictive control. However, in situations where the discretization error strongly depends on the applied control input, meeting accuracy and sampling time requirements simultaneously can be challenging using classical discretization methods. In particular, neither fixed-grid nor adaptive-grid discretizations may be suitable, when they suffer from large integration error or exceed the prescribed sampling time, respectively. In this work, we take a first step at closing this gap by utilizing probabilistic numerical integrators to approximate the solution of the initial value problem, as well as the computational uncertainty associated with it, inside the optimal control problem (OCP). By taking the viewpoint of probabilistic numerics and propagating the numerical uncertainty in the cost, the OCP is reformulated such that the optimal input reduces the computational uncertainty insofar as it is beneficial for the control objective. The proposed approach is illustrated using a numerical example, and potential benefits and limitations are discussed.},
note = {Submitted to the 6th Annual Learning for Dynamics & Control Conference (L4DC 2024)},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Appropriate time discretization is crucial for nonlinear model predictive control. However, in situations where the discretization error strongly depends on the applied control input, meeting accuracy and sampling time requirements simultaneously can be challenging using classical discretization methods. In particular, neither fixed-grid nor adaptive-grid discretizations may be suitable, when they suffer from large integration error or exceed the prescribed sampling time, respectively. In this work, we take a first step at closing this gap by utilizing probabilistic numerical integrators to approximate the solution of the initial value problem, as well as the computational uncertainty associated with it, inside the optimal control problem (OCP). By taking the viewpoint of probabilistic numerics and propagating the numerical uncertainty in the cost, the OCP is reformulated such that the optimal input reduces the computational uncertainty insofar as it is beneficial for the control objective. The proposed approach is illustrated using a numerical example, and potential benefits and limitations are discussed.
13.
Leeman, Antoine P.; Köhler, Johannes; Messerer, Florian; Lahr, Amon; Diehl, Moritz; Zeilinger, Melanie N.
Fast System Level Synthesis: Robust Model Predictive Control Using Riccati Recursions Working paper
2024, (Submitted to the 2024 IFAC Conference on Nonlinear Model Predictive Control (NMPC)).
@workingpaper{leeman_fast_2024,
title = {Fast System Level Synthesis: Robust Model Predictive Control Using Riccati Recursions},
author = {Antoine P. Leeman and Johannes Köhler and Florian Messerer and Amon Lahr and Moritz Diehl and Melanie N. Zeilinger},
url = {https://doi.org/10.48550/arXiv.2401.13762},
year = {2024},
date = {2024-02-07},
urldate = {2024-02-07},
abstract = {System Level Synthesis (SLS) enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem. The proposed algorithm builds on a recently proposed joint optimization scheme and iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of O(N2(n3x+n3u)) for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups of order 10 to 10^3 compared to general-purpose commercial solvers.
},
note = {Submitted to the 2024 IFAC Conference on Nonlinear Model Predictive Control (NMPC)},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
System Level Synthesis (SLS) enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem. The proposed algorithm builds on a recently proposed joint optimization scheme and iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of O(N2(n3x+n3u)) for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups of order 10 to 10^3 compared to general-purpose commercial solvers.
14.
Bonassi, Fabio; Bella, Alessio La; Farina, Marcello; Scattolini, Riccardo
Nonlinear MPC design for incrementally ISS systems with application to GRU networks Journal Article
In: Automatica, vol. 159, iss. 11381, pp. 111381, 2024.
@article{bonassi2024nonlinear,
title = {Nonlinear MPC design for incrementally ISS systems with application to GRU networks},
author = {Fabio Bonassi and Alessio La Bella and Marcello Farina and Riccardo Scattolini},
doi = {https://doi.org/10.1016/j.automatica.2023.111381},
year = {2024},
date = {2024-01-03},
urldate = {2024-01-03},
journal = {Automatica},
volume = {159},
issue = {11381},
pages = {111381},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
15.
Frey, Jonathan; Gao, Yunfan; Messerer, Florian; Lahr, Amon; Zeilinger, Melanie N.; Diehl, Moritz
Efficient Zero-Order Robust Optimization for Real-Time Model Predictive Control with Acados Working paper
2023.
@workingpaper{frey_efficient_2023,
title = {Efficient Zero-Order Robust Optimization for Real-Time Model Predictive Control with Acados},
author = {Jonathan Frey and Yunfan Gao and Florian Messerer and Amon Lahr and Melanie N. Zeilinger and Moritz Diehl},
doi = {10.48550/arXiv.2311.04557},
year = {2023},
date = {2023-12-18},
abstract = {Robust and stochastic optimal control problem (OCP) formulations allow a systematic treatment of uncertainty, but are typically associated with a high computational cost. The recently proposed zero-order robust optimization (zoRO) algorithm mitigates the computational cost of uncertainty-aware MPC by propagating the uncertainties outside of the MPC problem. This paper details the combination of zoRO with the real-time iteration (RTI) scheme and presents an efficient open-source implementation in acados, utilizing BLASFEO for the linear algebra operations. In addition to the scaling advantages posed by the zoRO algorithm, the efficient implementation drastically reduces the computational overhead, and, combined with an RTI scheme, enables the use of tube-based MPC for a wider range of applications. The flexibility, usability and effectiveness of the proposed implementation is demonstrated on two examples. On the practical example of a differential drive robot, the proposed implementation results in a tenfold reduction of computation time with respect to the previously available zoRO implementation.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Robust and stochastic optimal control problem (OCP) formulations allow a systematic treatment of uncertainty, but are typically associated with a high computational cost. The recently proposed zero-order robust optimization (zoRO) algorithm mitigates the computational cost of uncertainty-aware MPC by propagating the uncertainties outside of the MPC problem. This paper details the combination of zoRO with the real-time iteration (RTI) scheme and presents an efficient open-source implementation in acados, utilizing BLASFEO for the linear algebra operations. In addition to the scaling advantages posed by the zoRO algorithm, the efficient implementation drastically reduces the computational overhead, and, combined with an RTI scheme, enables the use of tube-based MPC for a wider range of applications. The flexibility, usability and effectiveness of the proposed implementation is demonstrated on two examples. On the practical example of a differential drive robot, the proposed implementation results in a tenfold reduction of computation time with respect to the previously available zoRO implementation.
16.
Roy, Wim Van; Nurkanovic, Armin; Abbasi-Esfeden, Ramin; Frey, Jonathan; Pozharskiy, Anton; Swevers, Jan; Diehl, Moritz
Continuous Optimization for Control of Finite-State Machines with Cascaded Hysteresis Via Time-Freezing Proceedings Article Forthcoming
In: 2023 Conference on Decision and Control (CDC), Forthcoming.
@inproceedings{VanRoy2023CDC,
title = {Continuous Optimization for Control of Finite-State Machines with Cascaded Hysteresis Via Time-Freezing},
author = {Wim Van Roy and Armin Nurkanovic and Ramin Abbasi-Esfeden and Jonathan Frey and Anton Pozharskiy and Jan Swevers and Moritz Diehl},
year = {2023},
date = {2023-12-01},
booktitle = {2023 Conference on Decision and Control (CDC)},
abstract = {Control problems with Finite-State Machines (FSM) are often solved using integer variables, leading to a mixed-integer optimal control problem (MIOCP). This paper proposes analternative method to describe a subclass of FSMs using complementarity constraints and time-freezing. The FSM from this subclass is built up by a sequence of states where a transition between the states is triggered by a single switching function. This can be looked at as a cascade of hysteresis loops where a memory effect is used to maintain the active state of the state machine. Based on the reformulation for hybrid systems with a hysteresis loop, a method is developed to reformulate this subclass in a similar fashion. The approach transforms the original problem into a Piecewise Smooth System (PSS), which can be discretized using the recently developed Finite Elements with Switch Detection, allowing for high-accuracy solutions. The reformation is compared to a mixed-integer formulation from the literature on a time-optimal control problem. This work is a first step towards the general reformulation of FSMs into nonsmooth systems without integer states.},
keywords = {},
pubstate = {forthcoming},
tppubtype = {inproceedings}
}
Control problems with Finite-State Machines (FSM) are often solved using integer variables, leading to a mixed-integer optimal control problem (MIOCP). This paper proposes analternative method to describe a subclass of FSMs using complementarity constraints and time-freezing. The FSM from this subclass is built up by a sequence of states where a transition between the states is triggered by a single switching function. This can be looked at as a cascade of hysteresis loops where a memory effect is used to maintain the active state of the state machine. Based on the reformulation for hybrid systems with a hysteresis loop, a method is developed to reformulate this subclass in a similar fashion. The approach transforms the original problem into a Piecewise Smooth System (PSS), which can be discretized using the recently developed Finite Elements with Switch Detection, allowing for high-accuracy solutions. The reformation is compared to a mixed-integer formulation from the literature on a time-optimal control problem. This work is a first step towards the general reformulation of FSMs into nonsmooth systems without integer states.
17.
Voogd, Kevin; Allamaa, Jean Pierre; Alonso-Mora, Javier; Son, Tong Duy
Reinforcement Learning from Simulation to Real World Autonomous Driving using Digital Twin Proceedings Article
In: 22nd IFAC World Congress 2023, pp. 1510-1515, Elsevier Ltd, Yokohama, Japan, 2023, ISSN: 2405-8963.
@inproceedings{Voogd2023ReinforcementLF,
title = {Reinforcement Learning from Simulation to Real World Autonomous Driving using Digital Twin},
author = {Kevin Voogd and Jean Pierre Allamaa and Javier Alonso-Mora and Tong Duy Son},
url = {https://www.sciencedirect.com/science/article/pii/S2405896323022553},
doi = {https://doi.org/10.1016/j.ifacol.2023.10.1846},
issn = {2405-8963},
year = {2023},
date = {2023-11-30},
urldate = {2023-11-30},
booktitle = {22nd IFAC World Congress 2023},
journal = {IFAC-PapersOnLine},
volume = {56},
number = {2},
pages = {1510-1515},
publisher = {Elsevier Ltd},
address = {Yokohama, Japan},
abstract = {Reinforcement learning (RL) is a promising solution for autonomous vehicles to deal with complex and uncertain traffic environments. The RL training process is however expensive, unsafe, and time-consuming. Algorithms are often developed first in simulation and then transferred to the real-world, leading to a common sim2real challenge where performance decreases when the domain changes. In this paper, we propose a transfer learning process to minimize the gap by exploiting digital twin technology, relying on a systematic and simultaneous combination of virtual and real world data coming from vehicle dynamics and traffic scenarios. The model and testing environment is evolved from model, hardware to vehicle in the loop and proving ground testing stages, similar to standard development cycle in the automotive industry. In particular, we also integrate other transfer learning techniques such as domain randomization and adaptation in each stage. The simulation and real data are gradually incorporated to accelerate and make the transfer learning process more robust. The proposed RL methodology is applied to develop a path-following steering controller for an autonomous electric vehicle. After learning and deploying the real-time RL control policy on the vehicle, we obtained satisfactory and safe control performance already from the first deployment, demonstrating the advantages of the proposed digital twin based learning process.
},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Reinforcement learning (RL) is a promising solution for autonomous vehicles to deal with complex and uncertain traffic environments. The RL training process is however expensive, unsafe, and time-consuming. Algorithms are often developed first in simulation and then transferred to the real-world, leading to a common sim2real challenge where performance decreases when the domain changes. In this paper, we propose a transfer learning process to minimize the gap by exploiting digital twin technology, relying on a systematic and simultaneous combination of virtual and real world data coming from vehicle dynamics and traffic scenarios. The model and testing environment is evolved from model, hardware to vehicle in the loop and proving ground testing stages, similar to standard development cycle in the automotive industry. In particular, we also integrate other transfer learning techniques such as domain randomization and adaptation in each stage. The simulation and real data are gradually incorporated to accelerate and make the transfer learning process more robust. The proposed RL methodology is applied to develop a path-following steering controller for an autonomous electric vehicle. After learning and deploying the real-time RL control policy on the vehicle, we obtained satisfactory and safe control performance already from the first deployment, demonstrating the advantages of the proposed digital twin based learning process.
18.
Acerbo, Flavia Sofia; Swevers, Jan; Tuytelaars, Tinne; Son, Tong Duy
Evaluation of MPC-based Imitation Learning for Human-like Autonomous Driving Proceedings Article
In: 22nd IFAC World Congress, pp. 4871-4876, Elsevier Ltd, Yokohama, Japan, 2023, ISSN: 2405-8963.
@inproceedings{acerboEvaluationMPCbasedImitation2023,
title = {Evaluation of MPC-based Imitation Learning for Human-like Autonomous Driving},
author = {Flavia Sofia Acerbo and Jan Swevers and Tinne Tuytelaars and Tong Duy Son},
url = {https://www.sciencedirect.com/science/article/pii/S2405896323016610},
doi = {https://doi.org/10.1016/j.ifacol.2023.10.1257},
issn = {2405-8963},
year = {2023},
date = {2023-11-30},
urldate = {2023-11-30},
booktitle = {22nd IFAC World Congress},
journal = { IFAC-PapersOnLine},
volume = {56},
number = {2},
pages = {4871-4876},
publisher = {Elsevier Ltd},
address = {Yokohama, Japan},
abstract = {This work evaluates and analyzes the combination of imitation learning (IL) and differentiable model predictive control (MPC) for the application of human-like autonomous driving. We combine MPC with a hierarchical learning-based policy, and measure its performance in open-loop and closed-loop with metrics related to safety, comfort and similarity to human driving characteristics. We also demonstrate the value of augmenting open-loop behavioral cloning with closed-loop training for a more robust learning, approximating the policy gradient through time with the state space model used by the MPC. We perform experimental evaluations on a lane keeping control system, learned from demonstrations collected on a fixed-base driving simulator, and show that our imitative policies approach the human driving style preferences.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
This work evaluates and analyzes the combination of imitation learning (IL) and differentiable model predictive control (MPC) for the application of human-like autonomous driving. We combine MPC with a hierarchical learning-based policy, and measure its performance in open-loop and closed-loop with metrics related to safety, comfort and similarity to human driving characteristics. We also demonstrate the value of augmenting open-loop behavioral cloning with closed-loop training for a more robust learning, approximating the policy gradient through time with the state space model used by the MPC. We perform experimental evaluations on a lane keeping control system, learned from demonstrations collected on a fixed-base driving simulator, and show that our imitative policies approach the human driving style preferences.
19.
Reiter, Rudolf; Nurkanovic, Armin; Frey, Jonathan; Diehl, Moritz
Frenet-Cartesian model representations for automotive obstacle avoidance within nonlinear MPC Journal Article
In: European Journal of Control, vol. 74, pp. 100847, 2023, ISSN: 0947-3580, (2023 European Control Conference Special Issue).
@article{REITER2023100847,
title = {Frenet-Cartesian model representations for automotive obstacle avoidance within nonlinear MPC},
author = {Rudolf Reiter and Armin Nurkanovic and Jonathan Frey and Moritz Diehl},
url = {https://www.sciencedirect.com/science/article/pii/S0947358023000766},
doi = {https://doi.org/10.1016/j.ejcon.2023.100847},
issn = {0947-3580},
year = {2023},
date = {2023-11-01},
journal = {European Journal of Control},
volume = {74},
pages = {100847},
abstract = {In recent years, nonlinear model predictive control has been extensively used for solving automotive motion control and planning tasks. In order to formulate the nonlinear model predictive control problem, different coordinate systems can be used with different advantages. We propose and compare formulations for the nonlinear MPC related optimization problem, involving a Cartesian and a Frenet coordinate frame in a single nonlinear program. We specify costs and collision avoidance constraints in the more advantageous coordinate frame, derive appropriate formulations and compare different obstacle constraints. With this approach, we exploit the simpler formulation of opponent vehicle constraints in the Cartesian coordinate frame, as well as road-aligned costs and constraints related to the Frenet coordinate frame. Comparisons to other approaches in a simulation framework highlight the advantages of the proposed methods.},
note = {2023 European Control Conference Special Issue},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In recent years, nonlinear model predictive control has been extensively used for solving automotive motion control and planning tasks. In order to formulate the nonlinear model predictive control problem, different coordinate systems can be used with different advantages. We propose and compare formulations for the nonlinear MPC related optimization problem, involving a Cartesian and a Frenet coordinate frame in a single nonlinear program. We specify costs and collision avoidance constraints in the more advantageous coordinate frame, derive appropriate formulations and compare different obstacle constraints. With this approach, we exploit the simpler formulation of opponent vehicle constraints in the Cartesian coordinate frame, as well as road-aligned costs and constraints related to the Frenet coordinate frame. Comparisons to other approaches in a simulation framework highlight the advantages of the proposed methods.
20.
Zhang, Yuan; Wang, Jianhong; Boedecker, Joschka
Robust Reinforcement Learning in Continuous Control Tasks with Uncertainty Set Regularization Proceedings Article
In: 7th Annual Conference on Robot Learning, 2023.
@inproceedings{zhang2023robust,
title = {Robust Reinforcement Learning in Continuous Control Tasks with Uncertainty Set Regularization},
author = {Yuan Zhang and Jianhong Wang and Joschka Boedecker},
url = {https://openreview.net/forum?id=keAPCON4jHC},
year = {2023},
date = {2023-10-16},
urldate = {2023-10-16},
booktitle = {7th Annual Conference on Robot Learning},
abstract = {Reinforcement learning (RL) is recognized as lacking generalization and robustness under environmental perturbations, which excessively restricts its application for real-world robotics. Prior work claimed that adding regularization to the value function is equivalent to learning a robust policy under uncertain transitions. Although the regularization-robustness transformation is appealing for its simplicity and efficiency, it is still lacking in continuous control tasks. In this paper, we propose a new regularizer named Uncertainty Set Regularizer (USR), to formulate the uncertainty set on the parametric space of a transition function. To deal with unknown uncertainty sets, we further propose a novel adversarial approach to generate them based on the value function. We evaluate USR on the Real-world Reinforcement Learning (RWRL) benchmark and the Unitree A1 Robot, demonstrating improvements in the robust performance of perturbed testing environments and sim-to-real scenarios.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Reinforcement learning (RL) is recognized as lacking generalization and robustness under environmental perturbations, which excessively restricts its application for real-world robotics. Prior work claimed that adding regularization to the value function is equivalent to learning a robust policy under uncertain transitions. Although the regularization-robustness transformation is appealing for its simplicity and efficiency, it is still lacking in continuous control tasks. In this paper, we propose a new regularizer named Uncertainty Set Regularizer (USR), to formulate the uncertainty set on the parametric space of a transition function. To deal with unknown uncertainty sets, we further propose a novel adversarial approach to generate them based on the value function. We evaluate USR on the Real-world Reinforcement Learning (RWRL) benchmark and the Unitree A1 Robot, demonstrating improvements in the robust performance of perturbed testing environments and sim-to-real scenarios.