Publications
1.
Gottardini, Andrea; Cecchin, Leonardo; Demir, Ozan; Fagiano, Lorenzo
Data-Driven Nonlinear Model Predictive Control for Grading Functions for Excavators Working paper Forthcoming
Forthcoming.
@workingpaper{gottardini_data-driven_2025,
title = {Data-Driven Nonlinear Model Predictive Control for Grading Functions for Excavators},
author = {Andrea Gottardini and Leonardo Cecchin and Ozan Demir and Lorenzo Fagiano},
year = {2025},
date = {2025-12-31},
abstract = {Hydraulic excavators are essential construc-
tion machines widely utilized for ground shaping tasks,
such as horizontal leveling and creating sloped surfaces.
These operations require a high degree of precision, which
can be challenging for unskilled workers.
The implementation of automation in hydraulic machin-
ery has the potential to significantly enhance productivity
by improving accuracy and reducing reliance on highly
trained labor. However, the control of hydraulic systems is
complicated by strong nonlinearities and variability among
machines, making the design of effective controllers a sig-
nificant challenge.
In this paper, we propose a data-driven Model Predictive
Control (MPC) system, initially developed for trajectory
tracking and subsequently adapted for a path following
approach. This adaptation is crucial because the trajectory
tracking method relies on open-loop references, using a
predefined speed profile that does not account for the
dynamics of the hydraulic excavator, potentially leading to
difficult-to-follow trajectories.
The prediction model used in the MPC is based on Linear
Local Neuro-Fuzzy Models, trained with the LOcal LInear
MOdel Tree (LOLIMOT) algorithm, while the linear parame-
ters are refined using the Simulation Error Method (SEM).
The proposed control system was rigorously tested on
a JCB Hydradig 110W following a comprehensive data
collection campaign to obtain the necessary data for the
data-driven model of the hydraulic cylinders.
Results, evaluated using metrics such as root mean
square error (RMSE) between the actual and reference
paths, maximum error, and standard deviation (indicating
oscillations during motion), demonstrate that our approach
outperforms previous data-driven feed-forward controllers,
highlighting its efficacy in enhancing hydraulic automation.},
keywords = {},
pubstate = {forthcoming},
tppubtype = {workingpaper}
}
Hydraulic excavators are essential construc-
tion machines widely utilized for ground shaping tasks,
such as horizontal leveling and creating sloped surfaces.
These operations require a high degree of precision, which
can be challenging for unskilled workers.
The implementation of automation in hydraulic machin-
ery has the potential to significantly enhance productivity
by improving accuracy and reducing reliance on highly
trained labor. However, the control of hydraulic systems is
complicated by strong nonlinearities and variability among
machines, making the design of effective controllers a sig-
nificant challenge.
In this paper, we propose a data-driven Model Predictive
Control (MPC) system, initially developed for trajectory
tracking and subsequently adapted for a path following
approach. This adaptation is crucial because the trajectory
tracking method relies on open-loop references, using a
predefined speed profile that does not account for the
dynamics of the hydraulic excavator, potentially leading to
difficult-to-follow trajectories.
The prediction model used in the MPC is based on Linear
Local Neuro-Fuzzy Models, trained with the LOcal LInear
MOdel Tree (LOLIMOT) algorithm, while the linear parame-
ters are refined using the Simulation Error Method (SEM).
The proposed control system was rigorously tested on
a JCB Hydradig 110W following a comprehensive data
collection campaign to obtain the necessary data for the
data-driven model of the hydraulic cylinders.
Results, evaluated using metrics such as root mean
square error (RMSE) between the actual and reference
paths, maximum error, and standard deviation (indicating
oscillations during motion), demonstrate that our approach
outperforms previous data-driven feed-forward controllers,
highlighting its efficacy in enhancing hydraulic automation.
tion machines widely utilized for ground shaping tasks,
such as horizontal leveling and creating sloped surfaces.
These operations require a high degree of precision, which
can be challenging for unskilled workers.
The implementation of automation in hydraulic machin-
ery has the potential to significantly enhance productivity
by improving accuracy and reducing reliance on highly
trained labor. However, the control of hydraulic systems is
complicated by strong nonlinearities and variability among
machines, making the design of effective controllers a sig-
nificant challenge.
In this paper, we propose a data-driven Model Predictive
Control (MPC) system, initially developed for trajectory
tracking and subsequently adapted for a path following
approach. This adaptation is crucial because the trajectory
tracking method relies on open-loop references, using a
predefined speed profile that does not account for the
dynamics of the hydraulic excavator, potentially leading to
difficult-to-follow trajectories.
The prediction model used in the MPC is based on Linear
Local Neuro-Fuzzy Models, trained with the LOcal LInear
MOdel Tree (LOLIMOT) algorithm, while the linear parame-
ters are refined using the Simulation Error Method (SEM).
The proposed control system was rigorously tested on
a JCB Hydradig 110W following a comprehensive data
collection campaign to obtain the necessary data for the
data-driven model of the hydraulic cylinders.
Results, evaluated using metrics such as root mean
square error (RMSE) between the actual and reference
paths, maximum error, and standard deviation (indicating
oscillations during motion), demonstrate that our approach
outperforms previous data-driven feed-forward controllers,
highlighting its efficacy in enhancing hydraulic automation.
2.
Msaad, Salim; Cecchin, Leonardo; Demir, Ozan; Fagiano, Lorenzo
Data-Driven Model Predictive Control of an Hydraulic Excavator via Local Model Networks Proceedings Article Forthcoming
In: 2025 American Control Conference (ACC), Forthcoming.
@inproceedings{msaad_data-driven_2025,
title = {Data-Driven Model Predictive Control of an Hydraulic Excavator via Local Model Networks},
author = {Salim Msaad and Leonardo Cecchin and Ozan Demir and Lorenzo Fagiano},
year = {2025},
date = {2025-07-01},
urldate = {2025-07-01},
publisher = {2025 American Control Conference (ACC)},
abstract = {A novel solution to control an hydraulic excavator during grading tasks is proposed, featuring a Model Predictive Controller designed using Local Model Networks (LMNs), i.e. linear time-invariant dynamic models averaged by nonlinear static functions. The Local Linear Models Tree (LoLiMoT) algorithm is employed to derive an LMN from experimental data of a real excavator. Then, a nonlinear MPC law is designed and implemented on the excavator’s embedded control system. To further improve the computational efficiency, a time-varying MPC law is designed as well, where the LMN is linearized in real-time using the previously computed optimal trajectory. Experimental results, conducted with the excavator in realworld conditions, show the effectiveness of both approaches in achieving performance comparable to state-of-the-art solutions, while utilizing a more compact dataset and without the need of the hydraulic cylinders’ pressure measurement.},
keywords = {},
pubstate = {forthcoming},
tppubtype = {inproceedings}
}
A novel solution to control an hydraulic excavator during grading tasks is proposed, featuring a Model Predictive Controller designed using Local Model Networks (LMNs), i.e. linear time-invariant dynamic models averaged by nonlinear static functions. The Local Linear Models Tree (LoLiMoT) algorithm is employed to derive an LMN from experimental data of a real excavator. Then, a nonlinear MPC law is designed and implemented on the excavator’s embedded control system. To further improve the computational efficiency, a time-varying MPC law is designed as well, where the LMN is linearized in real-time using the previously computed optimal trajectory. Experimental results, conducted with the excavator in realworld conditions, show the effectiveness of both approaches in achieving performance comparable to state-of-the-art solutions, while utilizing a more compact dataset and without the need of the hydraulic cylinders’ pressure measurement.
3.
Yang, Shaohui; Ohtsuka, Toshiyuki; Jones, Colin
Brunovsky Riccati Recursion for Linear Model Predictive Control Proceedings Article Forthcoming
In: Forthcoming.
@inproceedings{yang2025brunovsky,
title = {Brunovsky Riccati Recursion for Linear Model Predictive Control},
author = {Shaohui Yang and Toshiyuki Ohtsuka and Colin Jones },
year = {2025},
date = {2025-02-14},
keywords = {},
pubstate = {forthcoming},
tppubtype = {inproceedings}
}
4.
Yang, Shaohui; Ohtsuka, Toshiyuki; Plancher, Brian; Jones, Colin
Polynomial and Parallelizable Preconditioning of Linear Systems for Model Predictive Control and Beyond Working paper
2025.
@workingpaper{yang2025polynomial,
title = {Polynomial and Parallelizable Preconditioning of Linear Systems for Model Predictive Control and Beyond},
author = {Shaohui Yang and Toshiyuki Ohtsuka and Brian Plancher and Colin Jones},
year = {2025},
date = {2025-02-14},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
5.
Yang, Shaohui; Jones, Colin
Enhanced Numerical Techniques and Efficient Implementation for Brunovsky Form-Based Linear Model Predictive Control Working paper
2025.
@workingpaper{yang2025enhanced,
title = {Enhanced Numerical Techniques and Efficient Implementation for Brunovsky Form-Based Linear Model Predictive Control},
author = {Shaohui Yang and Colin Jones },
year = {2025},
date = {2025-02-14},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
6.
Zhang, Shuhao; Swevers, Jan
Robustified Time-optimal Point-to-point Motion Planning and Control under Uncertainty Working paper
2025.
@workingpaper{zhang2025robustified,
title = {Robustified Time-optimal Point-to-point Motion Planning and Control under Uncertainty},
author = {Shuhao Zhang and Jan Swevers },
doi = {https://doi.org/10.48550/arXiv.2501.14526},
year = {2025},
date = {2025-01-24},
abstract = {This paper proposes a novel approach to formulate time-optimal point-to-point motion planning and control under uncertainty. The approach defines a robustified two-stage Optimal Control Problem (OCP), in which stage 1, with a fixed time grid, is seamlessly stitched with stage 2, which features a variable time grid. Stage 1 optimizes not only the nominal trajectory, but also feedback gains and corresponding state covariances, which robustify constraints in both stages. The outcome is a minimized uncertainty in stage 1 and a minimized total motion time for stage 2, both contributing to the time optimality and safety of the total motion. A timely replanning strategy is employed to handle changes in constraints and maintain feasibility, while a tailored iterative algorithm is proposed for efficient, real-time OCP execution.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
This paper proposes a novel approach to formulate time-optimal point-to-point motion planning and control under uncertainty. The approach defines a robustified two-stage Optimal Control Problem (OCP), in which stage 1, with a fixed time grid, is seamlessly stitched with stage 2, which features a variable time grid. Stage 1 optimizes not only the nominal trajectory, but also feedback gains and corresponding state covariances, which robustify constraints in both stages. The outcome is a minimized uncertainty in stage 1 and a minimized total motion time for stage 2, both contributing to the time optimality and safety of the total motion. A timely replanning strategy is employed to handle changes in constraints and maintain feasibility, while a tailored iterative algorithm is proposed for efficient, real-time OCP execution.
7.
Abbasi-Esfeden, Ramin; Nurkanovic, Armin; Diehl, Moritz; Patrinos, Panagiotis; Swevers, Jan
2025.
@workingpaper{abbasiesfeden2025efficientmixedintegerformulationiterative,
title = {An Efficient Mixed-Integer Formulation and an Iterative Method for Optimal Control of Switched Systems Under Dwell Time Constraints},
author = {Ramin Abbasi-Esfeden and Armin Nurkanovic and Moritz Diehl and Panagiotis Patrinos and Jan Swevers},
url = {https://arxiv.org/abs/2501.05158},
year = {2025},
date = {2025-01-09},
abstract = {This paper presents an efficient Mixed-Integer Nonlinear Programming (MINLP) formulation for systems with discrete control inputs under dwell time constraints. By viewing such systems as a switched system, the problem is decomposed into a Sequence Optimization (SO) and a Switching Time Optimization (STO) -- the former providing the sequence of the switched system, and the latter calculating the optimal switching times. By limiting the feasible set of SO to subsequences of a master sequence, this formulation requires a small number of binary variables, independent of the number of time discretization nodes. This enables the proposed formulation to provide solutions efficiently, even for large numbers of time discretization nodes. To provide even faster solutions, an iterative algorithm is introduced to heuristically solve STO and SO. The proposed approaches are then showcased on four different switched systems and results demonstrate the efficiency of the MINLP formulation and the iterative algorithm.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
This paper presents an efficient Mixed-Integer Nonlinear Programming (MINLP) formulation for systems with discrete control inputs under dwell time constraints. By viewing such systems as a switched system, the problem is decomposed into a Sequence Optimization (SO) and a Switching Time Optimization (STO) -- the former providing the sequence of the switched system, and the latter calculating the optimal switching times. By limiting the feasible set of SO to subsequences of a master sequence, this formulation requires a small number of binary variables, independent of the number of time discretization nodes. This enables the proposed formulation to provide solutions efficiently, even for large numbers of time discretization nodes. To provide even faster solutions, an iterative algorithm is introduced to heuristically solve STO and SO. The proposed approaches are then showcased on four different switched systems and results demonstrate the efficiency of the MINLP formulation and the iterative algorithm.
8.
Kessler, Nicolas; Fagiano, Lorenzo
On gain scheduling trajectory stabilization for nonlinear systems: theoretical insights and experimental results Journal Article
In: International Journal of Robust and Nonlinear Control, 2025.
@article{kessler2024gain,
title = {On gain scheduling trajectory stabilization for nonlinear systems: theoretical insights and experimental results},
author = {Nicolas Kessler and Lorenzo Fagiano },
url = {https://onlinelibrary.wiley.com/doi/full/10.1002/rnc.7784},
doi = {https://doi.org/10.1002/rnc.7784},
year = {2025},
date = {2025-01-07},
journal = {International Journal of Robust and Nonlinear Control},
abstract = {Steering a nonlinear system from an initial state to a desired one is a common task in control. While a nominal trajectory can be obtained rather systematically using a model, for example via numerical optimization, heuristics, or reinforcement learning, the design of a computationally fast and reliable feedback control law that guarantees rev{bounded deviations around} the found trajectory can be much more involved.
An approach that does not require high online computational power and is well-accepted in industry is gain-scheduling.
The results presented here pertain to the rev{boundedness} guarantees and rev{the set of safe initial conditions} of gain scheduled control laws, based on subsequent linearizations along the reference trajectory. The approach bounds the uncertainty arising from the linearization process, builds polytopic sets of linear time varying systems covering the nonlinear dynamics along the trajectory, and exploits sufficient conditions rev{for the existence of a robust polyquadratic Lyapunov function} to attempt the derivation of the desired gain-scheduled controller, via the solution of Linear Matrix Inequalities (LMIs). A result to estimate an ellipsoidal rev{set of safe initial conditions} is provided too. Moreover, arbitrary scheduling strategies between the control gains are considered in the analysis, and the method can be used also to check/assess the rev{boundedness} properties obtained with an existing gain-scheduled law.
The approach is demonstrated experimentally on a small quadcopter, as well as in simulation to design a scheduled controller for a chemical reactor model and to validate an existing control law for a gantry crane model.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Steering a nonlinear system from an initial state to a desired one is a common task in control. While a nominal trajectory can be obtained rather systematically using a model, for example via numerical optimization, heuristics, or reinforcement learning, the design of a computationally fast and reliable feedback control law that guarantees rev{bounded deviations around} the found trajectory can be much more involved.
An approach that does not require high online computational power and is well-accepted in industry is gain-scheduling.
The results presented here pertain to the rev{boundedness} guarantees and rev{the set of safe initial conditions} of gain scheduled control laws, based on subsequent linearizations along the reference trajectory. The approach bounds the uncertainty arising from the linearization process, builds polytopic sets of linear time varying systems covering the nonlinear dynamics along the trajectory, and exploits sufficient conditions rev{for the existence of a robust polyquadratic Lyapunov function} to attempt the derivation of the desired gain-scheduled controller, via the solution of Linear Matrix Inequalities (LMIs). A result to estimate an ellipsoidal rev{set of safe initial conditions} is provided too. Moreover, arbitrary scheduling strategies between the control gains are considered in the analysis, and the method can be used also to check/assess the rev{boundedness} properties obtained with an existing gain-scheduled law.
The approach is demonstrated experimentally on a small quadcopter, as well as in simulation to design a scheduled controller for a chemical reactor model and to validate an existing control law for a gantry crane model.
An approach that does not require high online computational power and is well-accepted in industry is gain-scheduling.
The results presented here pertain to the rev{boundedness} guarantees and rev{the set of safe initial conditions} of gain scheduled control laws, based on subsequent linearizations along the reference trajectory. The approach bounds the uncertainty arising from the linearization process, builds polytopic sets of linear time varying systems covering the nonlinear dynamics along the trajectory, and exploits sufficient conditions rev{for the existence of a robust polyquadratic Lyapunov function} to attempt the derivation of the desired gain-scheduled controller, via the solution of Linear Matrix Inequalities (LMIs). A result to estimate an ellipsoidal rev{set of safe initial conditions} is provided too. Moreover, arbitrary scheduling strategies between the control gains are considered in the analysis, and the method can be used also to check/assess the rev{boundedness} properties obtained with an existing gain-scheduled law.
The approach is demonstrated experimentally on a small quadcopter, as well as in simulation to design a scheduled controller for a chemical reactor model and to validate an existing control law for a gantry crane model.
9.
Abbasi-Esfeden, Ramin; Plate, Christoph; Sager, Sebastian; Swevers, Jan
Dynamic Programming for Mixed Integer Optimal Control Problems with Dwell Time Constraints Working paper
2024.
@workingpaper{AbbasiEsfeden2024,
title = {Dynamic Programming for Mixed Integer Optimal Control Problems with Dwell Time Constraints},
author = {Ramin Abbasi-Esfeden and Christoph Plate and Sebastian Sager and Jan Swevers},
url = {http://dx.doi.org/10.2139/ssrn.5043263},
doi = {10.2139/ssrn.5043263},
year = {2024},
date = {2024-12-17},
journal = {Elsevier BV},
abstract = {This paper introduces Dynamic Programming (DP) as a method for solving the Combinatorial Integral Approximation (CIA) problem within the CIA decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs). Additionally, we incorporate general dwell time constraints into the DP framework. The proposed method is tested on three MIOCPs with a minimum dwell time constraint, and its performance is compared to the usage of the state-of-the-art general purpose solver GuRoBi (MILP) and to the tailored branch-and-bound (BnB) solver from the pycombina package. The results show that DP is more computationally efficient, and its flexible cost-to-go function formulation makes it suitable for handling cases where simple approximations of the relaxed solution are insufficient.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
This paper introduces Dynamic Programming (DP) as a method for solving the Combinatorial Integral Approximation (CIA) problem within the CIA decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs). Additionally, we incorporate general dwell time constraints into the DP framework. The proposed method is tested on three MIOCPs with a minimum dwell time constraint, and its performance is compared to the usage of the state-of-the-art general purpose solver GuRoBi (MILP) and to the tailored branch-and-bound (BnB) solver from the pycombina package. The results show that DP is more computationally efficient, and its flexible cost-to-go function formulation makes it suitable for handling cases where simple approximations of the relaxed solution are insufficient.
10.
Lahr, Amon; Näf, Joshua; Wabersich, Kim P.; Frey, Jonathan; Siehl, Pascal; Carron, Andrea; Diehl, Moritz; Zeilinger, Melanie N.
L4acados: Learning-based Models for Acados, Applied to Gaussian Process-Based Predictive Control Working paper
2024.
@workingpaper{lahr_l4acados_2024,
title = {L4acados: Learning-based Models for Acados, Applied to Gaussian Process-Based Predictive Control},
author = {Amon Lahr and Joshua Näf and Kim P. Wabersich and Jonathan Frey and Pascal Siehl and Andrea Carron and Moritz Diehl and Melanie N. Zeilinger},
doi = {10.48550/arXiv.2411.19258},
year = {2024},
date = {2024-11-28},
urldate = {2024-11-28},
abstract = {Incorporating learning-based models, such as Gaussian processes (GPs), into model predictive control (MPC) strategies can significantly improve control performance and online adaptation capabilities for real-world applications. Still, despite recent advances in numerical optimization and real-time GP inference, its widespread application is limited by the lack of an efficient and modular open-source implementation. This work aims at filling this gap by providing an efficient implementation of zero-order Gaussian process-based MPC in acados, as well as L4acados, a general framework for incorporating non-CasADi (learning-based) residual models in acados. By providing the required sensitivities via a user-defined Python module, L4acados enables the implementation of MPC controllers with learning-based residual models in acados, while supporting custom Jacobian approximations, as well as parallelization of sensitivity computations when preparing the quadratic subproblems. The computational efficiency of L4acados is benchmarked against available software using a neural network-based control example. Last, it is used demonstrate the performance of the zero-order GP-MPC method applied to two hardware examples: autonomous miniature racing, as well as motion control of a full-scale autonomous vehicle for an ISO lane change maneuver.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Incorporating learning-based models, such as Gaussian processes (GPs), into model predictive control (MPC) strategies can significantly improve control performance and online adaptation capabilities for real-world applications. Still, despite recent advances in numerical optimization and real-time GP inference, its widespread application is limited by the lack of an efficient and modular open-source implementation. This work aims at filling this gap by providing an efficient implementation of zero-order Gaussian process-based MPC in acados, as well as L4acados, a general framework for incorporating non-CasADi (learning-based) residual models in acados. By providing the required sensitivities via a user-defined Python module, L4acados enables the implementation of MPC controllers with learning-based residual models in acados, while supporting custom Jacobian approximations, as well as parallelization of sensitivity computations when preparing the quadratic subproblems. The computational efficiency of L4acados is benchmarked against available software using a neural network-based control example. Last, it is used demonstrate the performance of the zero-order GP-MPC method applied to two hardware examples: autonomous miniature racing, as well as motion control of a full-scale autonomous vehicle for an ISO lane change maneuver.
11.
Dong, Shiying; Ghezzi, Andrea; Harzer, Jakob; Frey, Jonathan; Gao, Bingzhao; Chen, Hong; Diehl, Moritz
Real-Time NMPC With Convex--Concave Constraints and Application to Eco-Driving Journal Article
In: IEEE Transactions on Control Systems Technology, 2024.
@article{dong2024real,
title = {Real-Time NMPC With Convex--Concave Constraints and Application to Eco-Driving},
author = {Shiying Dong and Andrea Ghezzi and Jakob Harzer and Jonathan Frey and Bingzhao Gao and Hong Chen and Moritz Diehl},
doi = {10.1109/TCST.2024.3494993},
year = {2024},
date = {2024-11-15},
journal = {IEEE Transactions on Control Systems Technology},
abstract = {In this brief, we propose a novel real-time numerical algorithm for solving nonlinear model predictive control (NMPC) with convex–concave constraints, which arise in various practical applications. Instead of requiring full convergence for each problem at every sampling time, the proposed algorithm, called real-time iteration sequential convex programming (RTI-SCP), solves only one convex subproblem but iterates as the problem evolves. Compared with previous methods, the RTI-SCP adopts a more refined approach by linearizing only the concave components of the constraints. It retains and efficiently utilizes all the underlying convex structures, thereby transforming subproblems into structured forms that can be solved using the existing tools. In addition, to the best of our knowledge, the widely investigated eco-driving control strategy for autonomous vehicles is now formulated for the first time into a convex–concave programming problem with strong theoretical properties. Eventually, the experimental results demonstrate that the proposed strategy can improve computational efficiency and overall control performance, and it is suitable for real-time implementation.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this brief, we propose a novel real-time numerical algorithm for solving nonlinear model predictive control (NMPC) with convex–concave constraints, which arise in various practical applications. Instead of requiring full convergence for each problem at every sampling time, the proposed algorithm, called real-time iteration sequential convex programming (RTI-SCP), solves only one convex subproblem but iterates as the problem evolves. Compared with previous methods, the RTI-SCP adopts a more refined approach by linearizing only the concave components of the constraints. It retains and efficiently utilizes all the underlying convex structures, thereby transforming subproblems into structured forms that can be solved using the existing tools. In addition, to the best of our knowledge, the widely investigated eco-driving control strategy for autonomous vehicles is now formulated for the first time into a convex–concave programming problem with strong theoretical properties. Eventually, the experimental results demonstrate that the proposed strategy can improve computational efficiency and overall control performance, and it is suitable for real-time implementation.
12.
Wang, Renzi; Acerbo, Flavia Sofia; Son, Tong Duy; Patrinos, Panagiotis
Imitation Learning from Observations: An Autoregressive Mixture of Experts Approach Working paper
2024.
@workingpaper{wang2024imitation,
title = {Imitation Learning from Observations: An Autoregressive Mixture of Experts Approach},
author = {Renzi Wang and Flavia Sofia Acerbo and Tong Duy Son and Panagiotis Patrinos},
url = {https://doi.org/10.48550/arXiv.2411.08232
},
year = {2024},
date = {2024-11-12},
abstract = {This paper presents a novel approach to imitation learning from observations, where an autoregressive mixture of experts model is deployed to fit the underlying policy. The parameters of the model are learned via a two-stage framework. By leveraging the existing dynamics knowledge, the first stage of the framework estimates the control input sequences and hence reduces the problem complexity. At the second stage, the policy is learned by solving a regularized maximum-likelihood estimation problem using the estimated control input sequences. We further extend the learning procedure by incorporating a Lyapunov stability constraint to ensure asymptotic stability of the identified model, for accurate multi-step predictions. The effectiveness of the proposed framework is validated using two autonomous driving datasets collected from human demonstrations, demonstrating its practical applicability in modelling complex nonlinear dynamics.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
This paper presents a novel approach to imitation learning from observations, where an autoregressive mixture of experts model is deployed to fit the underlying policy. The parameters of the model are learned via a two-stage framework. By leveraging the existing dynamics knowledge, the first stage of the framework estimates the control input sequences and hence reduces the problem complexity. At the second stage, the policy is learned by solving a regularized maximum-likelihood estimation problem using the estimated control input sequences. We further extend the learning procedure by incorporating a Lyapunov stability constraint to ensure asymptotic stability of the identified model, for accurate multi-step predictions. The effectiveness of the proposed framework is validated using two autonomous driving datasets collected from human demonstrations, demonstrating its practical applicability in modelling complex nonlinear dynamics.
13.
Zhang, Yuan; Hoffman, Jasper; Boedecker, Joschka
UDUC: An Uncertainty-driven Approach for Learning-based Robust Control Proceedings Article
In: ECAI 2024 - 27th European Conference on Artificial Intelligence - Including 13th Conference on Prestigious Applications of Intelligent Systems (PAIS 2024), pp. 4402-4409, IOS Press, Santiago de Compostela, Spain, 2024.
@inproceedings{zhang2024uduc,
title = {UDUC: An Uncertainty-driven Approach for Learning-based Robust Control},
author = {Yuan Zhang and Jasper Hoffman and Joschka Boedecker},
url = {https://arxiv.org/abs/2405.02598},
doi = {10.3233/FAIA241018},
year = {2024},
date = {2024-10-24},
urldate = {2024-10-24},
booktitle = {ECAI 2024 - 27th European Conference on Artificial Intelligence - Including 13th Conference on Prestigious Applications of Intelligent Systems (PAIS 2024)},
volume = {392},
pages = {4402-4409},
publisher = {IOS Press},
address = {Santiago de Compostela, Spain},
series = {Frontiers in Artificial Intelligence and Applications},
abstract = {Learning-based techniques have become popular in both model predictive control (MPC) and reinforcement learning (RL). Probabilistic ensemble (PE) models offer a promising approach for modelling system dynamics, showcasing the ability to capture uncertainty and scalability in high-dimensional control scenarios. However, PE models are susceptible to mode collapse, resulting in non-robust control when faced with environments slightly different from the training set. In this paper, we introduce the uncertainty-driven robust control (UDUC) loss as an alternative objective for training PE models, drawing inspiration from contrastive learning. We analyze the robustness of the UDUC loss through the lens of robust optimization and evaluate its performance on the challenging real-world reinforcement learning (RWRL) benchmark, which involves significant environmental mismatches between the training and testing environments.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Learning-based techniques have become popular in both model predictive control (MPC) and reinforcement learning (RL). Probabilistic ensemble (PE) models offer a promising approach for modelling system dynamics, showcasing the ability to capture uncertainty and scalability in high-dimensional control scenarios. However, PE models are susceptible to mode collapse, resulting in non-robust control when faced with environments slightly different from the training set. In this paper, we introduce the uncertainty-driven robust control (UDUC) loss as an alternative objective for training PE models, drawing inspiration from contrastive learning. We analyze the robustness of the UDUC loss through the lens of robust optimization and evaluate its performance on the challenging real-world reinforcement learning (RWRL) benchmark, which involves significant environmental mismatches between the training and testing environments.
14.
Acerbo, Flavia Sofia; Swevers, Jan; Tuytelaars, Tinne; Son, Tong Duy
Driving from Vision through Differentiable Optimal Control Proceedings Article
In: 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2153-0866, IEEE, Abu Dhabi, United Arab Emirates, 2024, ISBN: 979-8-3503-7770-5.
@inproceedings{acerbo24drividoc,
title = {Driving from Vision through Differentiable Optimal Control},
author = {Flavia Sofia Acerbo and Jan Swevers and Tinne Tuytelaars and Tong Duy Son},
url = {https://doi.org/10.48550/arXiv.2403.15102
},
doi = {10.1109/IROS58592.2024.10802306},
isbn = {979-8-3503-7770-5},
year = {2024},
date = {2024-10-01},
booktitle = {2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)},
pages = {2153-0866},
publisher = {IEEE},
address = {Abu Dhabi, United Arab Emirates},
abstract = {This paper proposes DriViDOC: a framework for Driving from Vision through Differentiable Optimal Control, and its application to learn autonomous driving controllers from human demonstrations. DriViDOC combines the automatic inference of relevant features from camera frames with the properties of nonlinear model predictive control (NMPC), such as constraint satisfaction. Our approach leverages the differentiability of parametric NMPC, allowing for end-to-end learning of the driving model from images to control. The model is trained on an offline dataset comprising various human demonstrations collected on a motion-base driving simulator. During online testing, the model demonstrates successful imitation of different driving styles, and the interpreted NMPC parameters provide insights into the achievement of specific driving behaviors. Our experimental results show that DriViDOC outperforms other methods involving NMPC and neural networks, exhibiting an average improvement of 20% in imitation scores.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
This paper proposes DriViDOC: a framework for Driving from Vision through Differentiable Optimal Control, and its application to learn autonomous driving controllers from human demonstrations. DriViDOC combines the automatic inference of relevant features from camera frames with the properties of nonlinear model predictive control (NMPC), such as constraint satisfaction. Our approach leverages the differentiability of parametric NMPC, allowing for end-to-end learning of the driving model from images to control. The model is trained on an offline dataset comprising various human demonstrations collected on a motion-base driving simulator. During online testing, the model demonstrates successful imitation of different driving styles, and the interpreted NMPC parameters provide insights into the achievement of specific driving behaviors. Our experimental results show that DriViDOC outperforms other methods involving NMPC and neural networks, exhibiting an average improvement of 20% in imitation scores.
15.
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.
16.
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.
17.
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.
18.
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.
19.
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.
20.
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.