Publications
21.
Cupo, Alessandro; Cecchin, Leonardo; Demir, Ozan; Fagiano, Lorenzo
Energy-Optimal Trajectory Planning for Semi-Autonomous Hydraulic Excavators Proceedings Article
In: 4th Modeling, Estimation and Control Conference (MECC), 2024.
@inproceedings{cupo_energy-optimal_2024,
title = {Energy-Optimal Trajectory Planning for Semi-Autonomous Hydraulic Excavators},
author = {Alessandro Cupo and Leonardo Cecchin and Ozan Demir and Lorenzo Fagiano},
year = {2024},
date = {2024-10-01},
publisher = {4th Modeling, Estimation and Control Conference (MECC)},
abstract = {An optimal trajectory planning approach for hydraulic excavator arms is presented, where the goal is to create trajectories that trade-off energy consumption and completion time. We develop a physics-based model of the excavator, which describes both the dynamics and the hydraulic system’s behavior. Further investigation of the Optimal Control Problem, used to create the trajectory, allows for discussion regarding the trade-off between power and time recovering a wide range of solutions based on the designer’s choice. Lastly, the problem is extended to include obstacle-avoidance constraints, creating a collision-free and efficient path.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
An optimal trajectory planning approach for hydraulic excavator arms is presented, where the goal is to create trajectories that trade-off energy consumption and completion time. We develop a physics-based model of the excavator, which describes both the dynamics and the hydraulic system’s behavior. Further investigation of the Optimal Control Problem, used to create the trajectory, allows for discussion regarding the trade-off between power and time recovering a wide range of solutions based on the designer’s choice. Lastly, the problem is extended to include obstacle-avoidance constraints, creating a collision-free and efficient path.
22.
Zhang, Shuhao; Swevers, Jan
Time-optimal Point-to-point Motion Planning: A Two-stage Approach Proceedings Article
In: 8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024, pp. 139-145, IFAC-PapersOnLine, Kyoto, Japan, 2024.
@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
https://www.sciencedirect.com/science/article/pii/S2405896324014010},
doi = {https://doi.org/10.1016/j.ifacol.2024.09.022},
year = {2024},
date = {2024-09-25},
urldate = {2024-04-16},
booktitle = {8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024},
volume = {58},
number = {18},
pages = {139-145},
publisher = {IFAC-PapersOnLine},
address = {Kyoto, Japan},
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.},
keywords = {},
pubstate = {published},
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.
23.
Allamaa, Jean Pierre; Patrinos, Panagiotis; Ohtsuka, Toshiyuki; Son, Tong Duy
Real-time MPC with Control Barrier Functions for Autonomous Driving using Safety Enhanced Collocation Best Paper Proceedings Article
In: 8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024, pp. 392-399, IFAC-PapersOnLine, Kyoto, Japan, 2024, (Preprint: https://doi.org/10.48550/arXiv.2401.06648).
@inproceedings{allamaa2024RTMPCCBF,
title = {Real-time MPC with Control Barrier Functions for Autonomous Driving using Safety Enhanced Collocation},
author = {Jean Pierre Allamaa and Panagiotis Patrinos and Toshiyuki Ohtsuka and Tong Duy Son},
url = {https://www.sciencedirect.com/science/article/pii/S240589632401437X},
doi = {https://doi.org/10.1016/j.ifacol.2024.09.058},
year = {2024},
date = {2024-09-25},
urldate = {2024-09-25},
booktitle = {8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024},
volume = {58},
number = {18},
pages = {392-399},
publisher = {IFAC-PapersOnLine},
address = {Kyoto, Japan},
abstract = {The autonomous driving industry is continuously dealing with safety-critical scenarios, and nonlinear model predictive control (NMPC) is a powerful control strategy for handling such situations. However, standard safety constraints are not scalable and require a long NMPC horizon. Moreover, the adoption of NMPC in the automotive industry is limited by the heavy computation of numerical optimization routines. To address those issues, this paper presents a real-time capable NMPC for automated driving in urban environments, using control barrier functions (CBFs). Furthermore, the designed NMPC is based on a novel collocation transcription approach, named RESAFE/COL, that allows to reduce the number of optimization variables while still guaranteeing the continuous time (nonlinear) inequality constraints satisfaction, through regional convex hull approximation. RESAFE/COL is proven to be 5 times faster than multiple shooting and more tractable for embedded hardware without a decrease in the performance, nor accuracy and safety of the numerical solution. We validate our NMPC-CBF with RESAFE/COL on digital twins of the vehicle and the urban environment and show the safe controller's ability to improve crash avoidance by 91%. Supplementary visual material can be found at https://youtu.be/_EnbfYwljp4.},
note = {Preprint: https://doi.org/10.48550/arXiv.2401.06648},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
The autonomous driving industry is continuously dealing with safety-critical scenarios, and nonlinear model predictive control (NMPC) is a powerful control strategy for handling such situations. However, standard safety constraints are not scalable and require a long NMPC horizon. Moreover, the adoption of NMPC in the automotive industry is limited by the heavy computation of numerical optimization routines. To address those issues, this paper presents a real-time capable NMPC for automated driving in urban environments, using control barrier functions (CBFs). Furthermore, the designed NMPC is based on a novel collocation transcription approach, named RESAFE/COL, that allows to reduce the number of optimization variables while still guaranteeing the continuous time (nonlinear) inequality constraints satisfaction, through regional convex hull approximation. RESAFE/COL is proven to be 5 times faster than multiple shooting and more tractable for embedded hardware without a decrease in the performance, nor accuracy and safety of the numerical solution. We validate our NMPC-CBF with RESAFE/COL on digital twins of the vehicle and the urban environment and show the safe controller's ability to improve crash avoidance by 91%. Supplementary visual material can be found at https://youtu.be/_EnbfYwljp4.
24.
Kessler, Nicolas; Fagiano, Lorenzo
On the design of terminal ingredients for linear time varying model predictive control: Theory and experimental application Proceedings Article
In: 8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024, pp. 263–268, IFAC-PapersOnLine, 2024, ISSN: 2405-8963.
@inproceedings{kessler2024design,
title = {On the design of terminal ingredients for linear time varying model predictive control: Theory and experimental application},
author = {Nicolas Kessler and Lorenzo Fagiano },
url = {https://www.sciencedirect.com/science/article/pii/S2405896324014204},
doi = {https://doi.org/10.1016/j.ifacol.2024.09.041},
issn = {2405-8963},
year = {2024},
date = {2024-09-25},
booktitle = {8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024},
number = {18},
issue = {58},
pages = {263--268},
publisher = {IFAC-PapersOnLine},
abstract = {The use of Linear Time Varying (LTV) Model Predictive Control (MPC) to stabilize a set of trajectories of a nonlinear system is considered. This technique has been successfully applied in simulations and experiments, but only few contributions investigate stability aspects and the essential involved quantities: the terminal penalty and terminal constraint. Deriving the former is not always thoroughly addressed or it is based on the -rather restrictive- assumption that the whole set of linearized dynamics is quadratically stabilizable. In this article, we propose Linear Matrix Inequality (LMI) conditions to co-design a gain-scheduled auxiliary feedback and Lyapunov function, used to derive offline terminal set conditions and a terminal penalty constraint for an LTV MPC scheme guaranteeing stability and recursive constraint satisfaction. Recent results by the authors are extended to the case of a varying stage cost, such that the controller can be tuned to meet time-varying trade-offs between tracking accuracy and input activity. The approach is demonstrated in embedded hardware running on a CrazyFlie drone.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
The use of Linear Time Varying (LTV) Model Predictive Control (MPC) to stabilize a set of trajectories of a nonlinear system is considered. This technique has been successfully applied in simulations and experiments, but only few contributions investigate stability aspects and the essential involved quantities: the terminal penalty and terminal constraint. Deriving the former is not always thoroughly addressed or it is based on the -rather restrictive- assumption that the whole set of linearized dynamics is quadratically stabilizable. In this article, we propose Linear Matrix Inequality (LMI) conditions to co-design a gain-scheduled auxiliary feedback and Lyapunov function, used to derive offline terminal set conditions and a terminal penalty constraint for an LTV MPC scheme guaranteeing stability and recursive constraint satisfaction. Recent results by the authors are extended to the case of a varying stage cost, such that the controller can be tuned to meet time-varying trade-offs between tracking accuracy and input activity. The approach is demonstrated in embedded hardware running on a CrazyFlie drone.
25.
Gao, Yunfan; Messerer, Florian; van Duijkeren, Niels; Houska, Boris; Diehl, Moritz
Real-Time-Feasible Collision-Free Motion Planning For Ellipsoidal Objects Proceedings Article Forthcoming
In: Forthcoming, (Accepted at the 2024 Conference on Decision and Control (CDC)).
@inproceedings{24_gao_realtimefeasible,
title = {Real-Time-Feasible Collision-Free Motion Planning For Ellipsoidal Objects},
author = {Yunfan Gao and Florian Messerer and Niels van Duijkeren and Boris Houska and Moritz Diehl},
doi = {https://doi.org/10.48550/arXiv.2409.12007},
year = {2024},
date = {2024-09-18},
abstract = {Online planning of collision-free trajectories is a fundamental task for robotics and self-driving car applications. This paper revisits collision avoidance between ellipsoidal objects using differentiable constraints. Two ellipsoids do not overlap if and only if the endpoint of the vector between the center points of the ellipsoids does not lie in the interior of the Minkowski sum of the ellipsoids. This condition is formulated using a parametric over-approximation of the Minkowski sum, which can be made tight in any given direction. The resulting collision avoidance constraint is included in an optimal control problem (OCP) and evaluated in comparison to the separating-hyperplane approach. Not only do we observe that the Minkowski-sum formulation is computationally more efficient in our experiments, but also that using pre-determined over-approximation parameters based on warm-start trajectories leads to a very limited increase in suboptimality. This gives rise to a novel real-time scheme for collision-free motion planning with model predictive control (MPC). Both the real-time feasibility and the effectiveness of the constraint formulation are demonstrated in challenging real-world experiments.},
note = {Accepted at the 2024 Conference on Decision and Control (CDC)},
keywords = {},
pubstate = {forthcoming},
tppubtype = {inproceedings}
}
Online planning of collision-free trajectories is a fundamental task for robotics and self-driving car applications. This paper revisits collision avoidance between ellipsoidal objects using differentiable constraints. Two ellipsoids do not overlap if and only if the endpoint of the vector between the center points of the ellipsoids does not lie in the interior of the Minkowski sum of the ellipsoids. This condition is formulated using a parametric over-approximation of the Minkowski sum, which can be made tight in any given direction. The resulting collision avoidance constraint is included in an optimal control problem (OCP) and evaluated in comparison to the separating-hyperplane approach. Not only do we observe that the Minkowski-sum formulation is computationally more efficient in our experiments, but also that using pre-determined over-approximation parameters based on warm-start trajectories leads to a very limited increase in suboptimality. This gives rise to a novel real-time scheme for collision-free motion planning with model predictive control (MPC). Both the real-time feasibility and the effectiveness of the constraint formulation are demonstrated in challenging real-world experiments.
26.
Kessler, Nicolas
Linear matrix inequality conditions for gain-scheduling and model predictive control PhD Thesis
2024.
@phdthesis{kessler2024phdthesis,
title = {Linear matrix inequality conditions for gain-scheduling and model predictive control},
author = {Nicolas Kessler},
url = {https://www.politesi.polimi.it/handle/10589/224812},
year = {2024},
date = {2024-09-17},
abstract = {This dissertation presents a novel approach to gain-scheduling model predictive control (MPC) for trajectory tracking on uncertain nonlinear systems, leveraging linear parameter-varying (LPV) models. A hierarchical scheme is developed, separating trajectory generation from stabilization using a 2-Degrees-of-Freedom (DoF) design. The focus of this thesis is the design of the feedback action, such that it guarantees tracking of the reference under bound satisfaction.
A key innovation is the graph-based gain-scheduling variable, enabling modular feedback application for online decisions. Nonlinearities are taken into account by extending the resulting LPV model with a polytopic uncertainty. Initially, a simple Linear Matrix Inequality (LMI) conditions are proposed to address stabilizability and later extended to address performance in an MPC scheme. Subsequently, it yields a novel method for the systematic design of the terminal ingredients for an LTV MPC. The LTV MPC is then extended to a robust tube-MPC with constraint satisfaction.
Efficient offline solvability of the resulting LMI conditions is addressed via the Alternating Direction Method of Multipliers (ADMM) to enable memory-efficient, distributed optimization.
The proposed LTV MPC scheme is computationally efficient online, because the optimal control problem is structured as a convex Quadratic Program (QP), that exploits its temporal evolution.
Simulation on a Continuously Stirred Tank Reactor (CSTR) and hardware implementation on a CrazyFlie drone demonstrate the approach's capability to stabilize nonlinear systems under disturbances and constraints with limited computing resources.
These advancements, combined with efficient offline LMI solving, promise broad applicability for safety-critical industrial systems.},
keywords = {},
pubstate = {published},
tppubtype = {phdthesis}
}
This dissertation presents a novel approach to gain-scheduling model predictive control (MPC) for trajectory tracking on uncertain nonlinear systems, leveraging linear parameter-varying (LPV) models. A hierarchical scheme is developed, separating trajectory generation from stabilization using a 2-Degrees-of-Freedom (DoF) design. The focus of this thesis is the design of the feedback action, such that it guarantees tracking of the reference under bound satisfaction.
A key innovation is the graph-based gain-scheduling variable, enabling modular feedback application for online decisions. Nonlinearities are taken into account by extending the resulting LPV model with a polytopic uncertainty. Initially, a simple Linear Matrix Inequality (LMI) conditions are proposed to address stabilizability and later extended to address performance in an MPC scheme. Subsequently, it yields a novel method for the systematic design of the terminal ingredients for an LTV MPC. The LTV MPC is then extended to a robust tube-MPC with constraint satisfaction.
Efficient offline solvability of the resulting LMI conditions is addressed via the Alternating Direction Method of Multipliers (ADMM) to enable memory-efficient, distributed optimization.
The proposed LTV MPC scheme is computationally efficient online, because the optimal control problem is structured as a convex Quadratic Program (QP), that exploits its temporal evolution.
Simulation on a Continuously Stirred Tank Reactor (CSTR) and hardware implementation on a CrazyFlie drone demonstrate the approach's capability to stabilize nonlinear systems under disturbances and constraints with limited computing resources.
These advancements, combined with efficient offline LMI solving, promise broad applicability for safety-critical industrial systems.
A key innovation is the graph-based gain-scheduling variable, enabling modular feedback application for online decisions. Nonlinearities are taken into account by extending the resulting LPV model with a polytopic uncertainty. Initially, a simple Linear Matrix Inequality (LMI) conditions are proposed to address stabilizability and later extended to address performance in an MPC scheme. Subsequently, it yields a novel method for the systematic design of the terminal ingredients for an LTV MPC. The LTV MPC is then extended to a robust tube-MPC with constraint satisfaction.
Efficient offline solvability of the resulting LMI conditions is addressed via the Alternating Direction Method of Multipliers (ADMM) to enable memory-efficient, distributed optimization.
The proposed LTV MPC scheme is computationally efficient online, because the optimal control problem is structured as a convex Quadratic Program (QP), that exploits its temporal evolution.
Simulation on a Continuously Stirred Tank Reactor (CSTR) and hardware implementation on a CrazyFlie drone demonstrate the approach's capability to stabilize nonlinear systems under disturbances and constraints with limited computing resources.
These advancements, combined with efficient offline LMI solving, promise broad applicability for safety-critical industrial systems.
27.
Simpson, Léo; Xie, Jing; Asprion, Jonas; Scattolini, Riccardo
A Learning-based Model Predictive Control Scheme with Application to Temperature Control Units Proceedings Article
In: 2024 IEEE Conference on Control Technology and Applications (CCTA), pp. 675-680, IEEE, Newcastle upon Tyne, United Kingdom, 2024, ISSN: 2768-0770.
@inproceedings{xie2024learningbased,
title = {A Learning-based Model Predictive Control Scheme with Application to Temperature Control Units},
author = {Léo Simpson and Jing Xie and Jonas Asprion and Riccardo Scattolini
},
url = {https://arxiv.org/abs/2402.05606},
doi = {10.1109/CCTA60707.2024.10666571},
issn = {2768-0770},
year = {2024},
date = {2024-09-11},
urldate = {2024-09-11},
booktitle = {2024 IEEE Conference on Control Technology and Applications (CCTA)},
pages = {675-680},
publisher = {IEEE},
address = {Newcastle upon Tyne, United Kingdom},
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.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
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.
28.
Gao, Yunfan; Messerer, Florian; van Duijkeren, Niels; Diehl, Moritz
Stochastic Model Predictive Control with Optimal Linear Feedback for Mobile Robots in Dynamic Environments Proceedings Article
In: 8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024, pp. 153-158, IFAC-PapersOnLine, 2024.
@inproceedings{24_gao_stochasticmpc,
title = {Stochastic Model Predictive Control with Optimal Linear Feedback for Mobile Robots in Dynamic Environments},
author = {Yunfan Gao and Florian Messerer and Niels van Duijkeren and Moritz Diehl},
doi = {https://doi.org/10.1016/j.ifacol.2024.09.024},
year = {2024},
date = {2024-09-03},
urldate = {2024-09-03},
booktitle = {8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024},
volume = {58},
number = {18},
pages = {153-158},
publisher = {IFAC-PapersOnLine},
abstract = {Robot navigation around humans can be a challenging problem since human movements are hard to predict. Stochastic model predictive control (MPC) can account for such uncertainties and approximately bound the probability of a collision to take place. In this paper, to counteract the rapidly growing human motion uncertainty over time, we incorporate state feedback in the stochastic MPC. This allows the robot to more closely track reference trajectories. To this end the feedback policy is left as a degree of freedom in the optimal control problem. The stochastic MPC with feedback is validated in simulation experiments and is compared against nominal MPC and stochastic MPC without feedback. The added computation time can be limited by reducing the number of additional variables for the feedback law with a small compromise in control performance.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Robot navigation around humans can be a challenging problem since human movements are hard to predict. Stochastic model predictive control (MPC) can account for such uncertainties and approximately bound the probability of a collision to take place. In this paper, to counteract the rapidly growing human motion uncertainty over time, we incorporate state feedback in the stochastic MPC. This allows the robot to more closely track reference trajectories. To this end the feedback policy is left as a degree of freedom in the optimal control problem. The stochastic MPC with feedback is validated in simulation experiments and is compared against nominal MPC and stochastic MPC without feedback. The added computation time can be limited by reducing the number of additional variables for the feedback law with a small compromise in control performance.
29.
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 Proceedings Article
In: 8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024, IFAC-PapersOnLine, 2024.
@inproceedings{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},
doi = {10.1016/j.ifacol.2024.09.027},
year = {2024},
date = {2024-09-01},
urldate = {2024-02-07},
booktitle = {8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024},
volume = {58},
number = {18},
publisher = {IFAC-PapersOnLine},
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.
},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
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.
30.
Allamaa, Jean Pierre; Patrinos, Panagiotis; Auweraer, Herman Van; Son, Tong Duy
Learning-Based NMPC Adaptation for Autonomous Driving Using Parallelized Digital Twin Journal Article
In: IEEE Transactions on Control Systems Technology, vol. Early Access, pp. 1-16, 2024, ISSN: 1063-6536, (Preprint: https://doi.org/10.48550/arXiv.2402.16645).
@article{allamaa2024lbMPC,
title = {Learning-Based NMPC Adaptation for Autonomous Driving Using Parallelized Digital Twin},
author = {Jean Pierre Allamaa and Panagiotis Patrinos and Herman Van Auweraer and Tong Duy Son},
doi = {10.1109/TCST.2024.3437163},
issn = {1063-6536},
year = {2024},
date = {2024-08-14},
urldate = {2024-05-29},
journal = {IEEE Transactions on Control Systems Technology},
volume = {Early Access},
pages = {1-16},
abstract = {In this work, we focus on the challenge of transferring an autonomous driving (AD) controller from simulation to reality (Sim2Real). We propose a data-efficient method for online and on-the-fly adaptation of parametrizable control architectures such that the target closed-loop performance is optimized while accounting for uncertainties such as model mismatches, changes in the environment, and task variations. The novelty of the approach resides in leveraging black-box optimization enabled by executable digital twins (xDTs) for data-driven parameter calibration through derivative-free methods to directly adapt the controller in real time (RT). The xDTs are augmented with domain randomization (DR) for robustness and allow for safe parameter exploration. The proposed method requires a minimal amount of interaction with the real world as it pushes the exploration toward the xDTs. We validate our approach through real-world experiments, demonstrating its effectiveness in transferring and fine-tuning a nonlinear model predictive control (NMPC) with nine parameters, in under 10 min. This eliminates the need for hours-long manual tuning and lengthy machine learning training and data collection phases. Our results show that the online adapted NMPC directly compensates for the Sim2Real gap and avoids overtuning in simulation. Importantly, a 75% improvement in tracking performance is achieved, and the Sim2Real gap over the target performance is reduced from a factor of 876 to 1.033.},
note = {Preprint: https://doi.org/10.48550/arXiv.2402.16645},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this work, we focus on the challenge of transferring an autonomous driving (AD) controller from simulation to reality (Sim2Real). We propose a data-efficient method for online and on-the-fly adaptation of parametrizable control architectures such that the target closed-loop performance is optimized while accounting for uncertainties such as model mismatches, changes in the environment, and task variations. The novelty of the approach resides in leveraging black-box optimization enabled by executable digital twins (xDTs) for data-driven parameter calibration through derivative-free methods to directly adapt the controller in real time (RT). The xDTs are augmented with domain randomization (DR) for robustness and allow for safe parameter exploration. The proposed method requires a minimal amount of interaction with the real world as it pushes the exploration toward the xDTs. We validate our approach through real-world experiments, demonstrating its effectiveness in transferring and fine-tuning a nonlinear model predictive control (NMPC) with nine parameters, in under 10 min. This eliminates the need for hours-long manual tuning and lengthy machine learning training and data collection phases. Our results show that the online adapted NMPC directly compensates for the Sim2Real gap and avoids overtuning in simulation. Importantly, a 75% improvement in tracking performance is achieved, and the Sim2Real gap over the target performance is reduced from a factor of 876 to 1.033.
31.
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 Proceedings Article
In: 2024 IEEE International Conference on Robotics and Automation (ICRA), pp. 14258-14264, IEEE, Yokohama, Japan, 2024, ISBN: 979-8-3503-8457-4.
@inproceedings{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},
doi = {10.1109/ICRA57147.2024.10610134},
isbn = {979-8-3503-8457-4},
year = {2024},
date = {2024-08-08},
urldate = {2024-02-07},
booktitle = {2024 IEEE International Conference on Robotics and Automation (ICRA)},
pages = {14258-14264},
publisher = {IEEE},
address = {Yokohama, Japan},
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, even when subjected to disturbances, which are modeled as random process noise 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 disturbances. Both of these contributions are integrated into a robustified motion planning and control pipeline, the efficacy of which is validated through simulation experiments.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
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, even when subjected to disturbances, which are modeled as random process noise 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 disturbances. Both of these contributions are integrated into a robustified motion planning and control pipeline, the efficacy of which is validated through simulation experiments.
32.
Schulz, Felix; Hoffman, Jasper; Zhang, Yuan; Boedecker, Joschka
Learning When to Trust the Expert for Guided Exploration in RL Workshop
2024, (ICML 2024 Workshop: Foundations of Reinforcement Learning and Control -- Connections and Perspectives).
@workshop{schulz2024learning,
title = {Learning When to Trust the Expert for Guided Exploration in RL},
author = {Felix Schulz and Jasper Hoffman and Yuan Zhang and Joschka Boedecker },
url = {https://openreview.net/forum?id=QkTANn4mRa},
year = {2024},
date = {2024-08-07},
urldate = {2025-08-07},
abstract = {Reinforcement learning (RL) algorithms often rely on trial and error for exploring environments, leading to local minima and high sample inefficiency during training. In many cases, leveraging prior knowledge can efficiently construct expert policies, e.g. model predictive control (MPC) techniques. However, the expert might not be optimal and thus, when used as a prior, might introduce bias that can harm the control performance. Thus, in this work, we propose a novel RL method based on a simple options framework that only uses the expert to guide the exploration during training. The exploration is controlled by a learned high-level policy that can decide to follow either an expert policy or a learned low-level policy. In that sense, the high-level skip policy learns when to trust the expert for exploration. As we aim at deploying the low-level policy without accessing the expert after training, we increasingly regularize the usage of the expert during training, to reduce the covariate shift problem. Using different environments combined with potentially sub-optimal experts derived from MPC or RL, we find that our method improves over sub-optimal experts and significantly improves the sample efficiency.},
note = {ICML 2024 Workshop: Foundations of Reinforcement Learning and Control -- Connections and Perspectives},
keywords = {},
pubstate = {published},
tppubtype = {workshop}
}
Reinforcement learning (RL) algorithms often rely on trial and error for exploring environments, leading to local minima and high sample inefficiency during training. In many cases, leveraging prior knowledge can efficiently construct expert policies, e.g. model predictive control (MPC) techniques. However, the expert might not be optimal and thus, when used as a prior, might introduce bias that can harm the control performance. Thus, in this work, we propose a novel RL method based on a simple options framework that only uses the expert to guide the exploration during training. The exploration is controlled by a learned high-level policy that can decide to follow either an expert policy or a learned low-level policy. In that sense, the high-level skip policy learns when to trust the expert for exploration. As we aim at deploying the low-level policy without accessing the expert after training, we increasingly regularize the usage of the expert during training, to reduce the covariate shift problem. Using different environments combined with potentially sub-optimal experts derived from MPC or RL, we find that our method improves over sub-optimal experts and significantly improves the sample efficiency.
33.
Messerer, Florian; Baumgärtner, Katrin; Nurkanovic, Armin; Diehl, Moritz
Approximate propagation of normal distributions for stochastic optimal control of nonsmooth systems Journal Article
In: Nonlinear Analysis: Hybrid Systems, vol. 53, pp. 101499, 2024, ISSN: 1751-570X.
@article{MESSERER2024101499,
title = {Approximate propagation of normal distributions for stochastic optimal control of nonsmooth systems},
author = {Florian Messerer and Katrin Baumgärtner and Armin Nurkanovic and Moritz Diehl},
url = {https://www.sciencedirect.com/science/article/pii/S1751570X24000360},
doi = {https://doi.org/10.1016/j.nahs.2024.101499},
issn = {1751-570X},
year = {2024},
date = {2024-08-01},
urldate = {2023-08-14},
journal = {Nonlinear Analysis: Hybrid Systems},
volume = {53},
pages = {101499},
abstract = {We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinuous right-hand side. For piecewise affine systems, a normalization of the propagated probability distribution at every time step allows us to analytically compute the expectation integrals of the mean and covariance dynamics while explicitly taking into account the discontinuity. This leads to a natural smoothing of the discontinuity such that for relevant levels of uncertainty the resulting ODE can be integrated directly with standard schemes and it is neither necessary to prespecify the switching sequence nor to use a switch detection method. We then show how this result can be employed in the more general case of piecewise smooth functions based on a structure preserving linearization scheme. The resulting dynamics can be straightforwardly used within standard formulations of stochastic optimal control problems with chance constraints.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinuous right-hand side. For piecewise affine systems, a normalization of the propagated probability distribution at every time step allows us to analytically compute the expectation integrals of the mean and covariance dynamics while explicitly taking into account the discontinuity. This leads to a natural smoothing of the discontinuity such that for relevant levels of uncertainty the resulting ODE can be integrated directly with standard schemes and it is neither necessary to prespecify the switching sequence nor to use a switch detection method. We then show how this result can be employed in the more general case of piecewise smooth functions based on a structure preserving linearization scheme. The resulting dynamics can be straightforwardly used within standard formulations of stochastic optimal control problems with chance constraints.
34.
Cecchin, Leonardo; Trachte, Adrian; Fagiano, Lorenzo; Diehl, Moritz
Real-time prediction of human-generated reference signals for advanced digging control Proceedings Article
In: pp. 496–501, IEEE, Bari, IT, 2024.
@inproceedings{cecchin_real-time_2024,
title = {Real-time prediction of human-generated reference signals for advanced digging control},
author = {Leonardo Cecchin and Adrian Trachte and Lorenzo Fagiano and Moritz Diehl},
doi = {10.1109/CASE59546.2024.10711371},
year = {2024},
date = {2024-08-01},
pages = {496–501},
publisher = {IEEE},
address = {Bari, IT},
abstract = {In the realm of excavator control, advanced techniques, such as Model Predictive Control (MPC) and two-degrees-of-freedom structures (feedforward plus feedback), proved to have great potential for enhancing efficiency and performance. These methods rely on the knowledge of future reference, which is often pre-defined, to optimize the system behavior as a function of it. However, this assumption fails in applications where a human operator chooses the reference at runtime, such as in the case of non-autonomous digging operations. 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.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
In the realm of excavator control, advanced techniques, such as Model Predictive Control (MPC) and two-degrees-of-freedom structures (feedforward plus feedback), proved to have great potential for enhancing efficiency and performance. These methods rely on the knowledge of future reference, which is often pre-defined, to optimize the system behavior as a function of it. However, this assumption fails in applications where a human operator chooses the reference at runtime, such as in the case of non-autonomous digging operations. 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.
35.
Cecchin, Leonardo; Ohtsuka, Toshiyuki; Trachte, Adrian; Diehl, Moritz
Model Predictive Controller for Hydraulic Cylinders with Independent Metering Control Valves Proceedings Article
In: IFAC-PapersOnLine, pp. 281–287, IFAC, Kyoto, JP, 2024.
@inproceedings{cecchin_model_2024,
title = {Model Predictive Controller for Hydraulic Cylinders with Independent Metering Control Valves},
author = {Leonardo Cecchin and Toshiyuki Ohtsuka and Adrian Trachte and Moritz Diehl},
url = {https://www.sciencedirect.com/science/article/pii/S240589632401423X},
doi = {10.1016/j.ifacol.2024.09.044},
year = {2024},
date = {2024-08-01},
booktitle = {IFAC-PapersOnLine},
volume = {58},
pages = {281–287},
publisher = {IFAC},
address = {Kyoto, JP},
series = {18},
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 (acados). 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.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
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 (acados). 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.
36.
Lahr, Amon; Tronarp, Filip; Schmidt, Nathanael Bosch Jonathan; Hennig, Philipp; Zeilinger, Melanie N.
Probabilistic ODE Solvers for Integration Error-Aware Numerical Optimal Control Proceedings Article
In: Proceedings of the 6th Annual Learning for Dynamics & Control Conference (L4DC), pp. 1018–1032, PMLR, 2024.
@inproceedings{lahr_probabilistic_2024,
title = {Probabilistic ODE Solvers for Integration Error-Aware Numerical Optimal Control},
author = {Amon Lahr and Filip Tronarp and Nathanael Bosch Jonathan Schmidt and Philipp Hennig and Melanie N. Zeilinger},
url = {https://proceedings.mlr.press/v242/lahr24a.html
https://proceedings.mlr.press/v242/lahr24a/lahr24a.pdf},
year = {2024},
date = {2024-07-15},
urldate = {2024-02-07},
booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference (L4DC)},
volume = {242},
pages = {1018--1032},
publisher = {PMLR},
series = {Proceedings of Machine Learning Research},
abstract = {Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if 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.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if 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.
37.
Hoffman, Jasper; Clausen, Diego Fernandez; Brosseit, Julien; Bernhard, Julian; Esterle, Klemens; Werling, Moritz; Karg, Michael; Boedecker, Joschka
PlanNetX: Learning an efficient neural network planner from MPC for longitudinal control Proceedings Article
In: Proceedings of the 6th Annual Learning for Dynamics & Control Conference, pp. 1214-1227, PMLR, 2024.
@inproceedings{hoffmann_plannetx_2024,
title = {PlanNetX: Learning an efficient neural network planner from MPC for longitudinal control},
author = {Jasper Hoffman and Diego Fernandez Clausen and Julien Brosseit and Julian Bernhard and Klemens Esterle and Moritz Werling and Michael Karg and Joschka Boedecker},
url = {https://proceedings.mlr.press/v242/hoffmann24a.html
https://proceedings.mlr.press/v242/hoffmann24a/hoffmann24a.pdf},
year = {2024},
date = {2024-07-15},
urldate = {2024-07-15},
booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference},
pages = {1214-1227},
publisher = {PMLR},
series = {Proceedings of Machine Learning Research},
abstract = {Model predictive control (MPC) is a powerful, optimization-based approach for controlling dynamical systems. However, the computational complexity of online optimization can be problematic on embedded devices. Especially, when we need to guarantee fixed control frequencies. Thus, previous work proposed to reduce the computational burden using imitation learning (IL) approximating the MPC policy by a neural network. In this work, we instead learn the whole planned trajectory of the MPC. We introduce a combination of a novel neural network architecture PlanNetX and a simple loss function based on the state trajectory that leverages the parameterized optimal control structure of the MPC. We validate our approach in the context of autonomous driving by learning a longitudinal planner and benchmarking it extensively in the CommonRoad simulator using synthetic scenarios and scenarios derived from real data. Our experimental results show that we can learn the open-loop MPC trajectory with high accuracy while improving the closed-loop performance of the learned control policy over other baselines like behavior cloning.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Model predictive control (MPC) is a powerful, optimization-based approach for controlling dynamical systems. However, the computational complexity of online optimization can be problematic on embedded devices. Especially, when we need to guarantee fixed control frequencies. Thus, previous work proposed to reduce the computational burden using imitation learning (IL) approximating the MPC policy by a neural network. In this work, we instead learn the whole planned trajectory of the MPC. We introduce a combination of a novel neural network architecture PlanNetX and a simple loss function based on the state trajectory that leverages the parameterized optimal control structure of the MPC. We validate our approach in the context of autonomous driving by learning a longitudinal planner and benchmarking it extensively in the CommonRoad simulator using synthetic scenarios and scenarios derived from real data. Our experimental results show that we can learn the open-loop MPC trajectory with high accuracy while improving the closed-loop performance of the learned control policy over other baselines like behavior cloning.
38.
Pas, Pieter; Løwenstein, Kristoffer Fink; Bernardini, Daniele; Patrinos, Panagiotis
Exploiting Parallelism in a QPALM-based Solver for Optimal Control Workshop
2024, (RSS 2024 workshop: Frontiers of optimization for robotics).
@workshop{PasQPALMOCP,
title = {Exploiting Parallelism in a QPALM-based Solver for Optimal Control },
author = {Pieter Pas and Kristoffer Fink Løwenstein and Daniele Bernardini and Panagiotis Patrinos},
year = {2024},
date = {2024-07-14},
urldate = {2024-07-14},
note = {RSS 2024 workshop: Frontiers of optimization for robotics},
keywords = {},
pubstate = {published},
tppubtype = {workshop}
}
39.
Wang, Renzi; Bodard, Alexander; Schuurmans, Mathijs; Patrinos, Panagiotis
EM++: A parameter learning framework for stochastic switching systems Working paper
2024.
@workingpaper{wang2024em++,,
title = {EM++: A parameter learning framework for stochastic switching systems},
author = {Renzi Wang and Alexander Bodard and Mathijs Schuurmans and Panagiotis Patrinos},
url = {https://doi.org/10.48550/arXiv.2407.16359
},
year = {2024},
date = {2024-07-01},
abstract = {This paper proposes a general switching dynamical system model, and a custom majorization-minimization-based algorithm EM++ for identifying its parameters. For certain families of distributions, such as Gaussian distributions, this algorithm reduces to the well-known expectation-maximization method. We prove global convergence of the algorithm under suitable assumptions, thus addressing an important open issue in the switching system identification literature. The effectiveness of both the proposed model and algorithm is validated through extensive numerical experiments.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
This paper proposes a general switching dynamical system model, and a custom majorization-minimization-based algorithm EM++ for identifying its parameters. For certain families of distributions, such as Gaussian distributions, this algorithm reduces to the well-known expectation-maximization method. We prove global convergence of the algorithm under suitable assumptions, thus addressing an important open issue in the switching system identification literature. The effectiveness of both the proposed model and algorithm is validated through extensive numerical experiments.
40.
Zhang, Yuan; Yang, Shaohui; Ohtsuka, Toshiyuki; Jones, Colin; Boedecker, Joschka
Latent Linear Quadratic Regulator for Robotic Control Tasks Working paper
2024, (RSS 2024 Workshop on Koopman Operators in Robotics).
@workingpaper{zhang2024latent,
title = {Latent Linear Quadratic Regulator for Robotic Control Tasks},
author = {Yuan Zhang and Shaohui Yang and Toshiyuki Ohtsuka and Colin Jones and Joschka Boedecker},
url = {https://arxiv.org/abs/2407.11107},
year = {2024},
date = {2024-07-01},
urldate = {2024-07-01},
booktitle = {RSS 2024 Workshop on Koopman Operators in Robotics},
abstract = {Model predictive control (MPC) has played a more crucial role in various robotic control tasks, but its high computational requirements are concerning, especially for nonlinear dynamical models. This paper presents a latent linear quadratic regulator (LaLQR) that maps the state space into a latent space, on which the dynamical model is linear and the cost function is quadratic, allowing the efficient application of LQR. We jointly learn this alternative system by imitating the original MPC. Experiments show LaLQR's superior efficiency and generalization compared to other baselines.},
note = {RSS 2024 Workshop on Koopman Operators in Robotics},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Model predictive control (MPC) has played a more crucial role in various robotic control tasks, but its high computational requirements are concerning, especially for nonlinear dynamical models. This paper presents a latent linear quadratic regulator (LaLQR) that maps the state space into a latent space, on which the dynamical model is linear and the cost function is quadratic, allowing the efficient application of LQR. We jointly learn this alternative system by imitating the original MPC. Experiments show LaLQR's superior efficiency and generalization compared to other baselines.