Joseph Lorenzetti

ASL Publications

A. McClellan, J. Lorenzetti, M. Pavone, and C. Farhat, “A Physics-Based Digital Twin for Model Predictive Control of Autonomous Unmanned Aerial Vehicle Landing,” Philosophical Transactions of the Royal Society A, vol. 380, 2022.
[BibTeX] [Abstract]

Abstract: This paper proposes a two-level, data-driven, digital twin concept for the autonomous landing of aircraft, under some assumptions. It features a digital twin instance for model predictive control; and an innovative, real-time, digital twin prototype for fluid-structure interaction and flight dynamics to inform it. The latter digital twin is based on the linearization about a pre-designed glideslope trajectory of a high-fidelity, viscous, nonlinear computational model for flight dynamics; and its projection onto a low-dimensional approximation subspace to achieve real-time performance, while maintaining accuracy. Its main purpose is to predict in real-time, during flight, the state of an aircraft and the aerodynamic forces and moments acting on it. Unlike static lookup tables or regression-based surrogate models based on steady-state wind tunnel data, the aforementioned real-time digital twin prototype allows the digital twin instance for model predictive control to be informed by a truly dynamic flight model, rather than a less accurate set of steady-state aerodynamic force and moment data points. The paper describes in details the construction of the proposed two-level digital twin concept and its verification by numerical simulation. It also reports on its preliminary flight validation in autonomous mode for an off-the-shelf unmanned aerial vehicle instrumented at Stanford University.
```
@article{McClellanLorenzettiEtAl2021,
  author = {McClellan, A. and Lorenzetti, J. and Pavone, M. and Farhat, C.},
  title = {A Physics-Based Digital Twin for Model Predictive Control of Autonomous Unmanned Aerial Vehicle Landing},
  journal = {{Philosophical Transactions of the Royal Society A}},
  volume = {380},
  keywords = {pub},
  year = {2022},
  url = {/wp-content/papercite-data/pdf/McClellan.Lorenzetti.ea.PTRSA21.pdf},
  owner = {jlorenze},
  timestamp = {2021-11-11}
}
```
J. Lorenzetti, A. McClellan, C. Farhat, and M. Pavone, “Linear Reduced-Order Model Predictive Control,” IEEE Transactions on Automatic Control, vol. 67, no. 11, pp. 5980–5995, 2022.
[BibTeX] [Abstract]

Abstract: Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless, high-dimensional models arise in many settings, for example, discretization methods for generating finite-dimensional approximations to partial differential equations can result in models with thousands to millions of dimensions. In such cases, reduced-order models (ROMs) can significantly reduce computational requirements, but model approximation error must be considered to guarantee controller performance. In this article, a reduced-order model predictive control (ROMPC) scheme is proposed to solve robust, output feedback, constrained optimal control problems for high-dimensional linear systems. Computational efficiency is obtained by using projection-based ROMs, and guarantees on robust constraint satisfaction and stability are provided. The performance of the approach is demonstrated in simulation for several examples, including an aircraft control problem leveraging an inviscid computational fluid dynamics model with dimension 998 930.
```
@article{LorenzettiMcClellanEtAl2022,
  author = {Lorenzetti, J. and McClellan, A. and Farhat, C. and Pavone, M.},
  title = {Linear Reduced-Order Model Predictive Control},
  journal = {{IEEE Transactions on Automatic Control}},
  volume = {67},
  number = {11},
  pages = {5980--5995},
  year = {2022},
  keywords = {pub},
  owner = {rdyro},
  timestamp = {2022-10-27},
  url = {https://arxiv.org/abs/2012.03384}
}
```
J. Lorenzetti, “Reduced Order Model Predictive Control of High-Dimensional Systems,” PhD thesis, Stanford University, Dept. of Aeronautics and Astronautics, Stanford, California, 2021.
[BibTeX] [Abstract]

Abstract: Many physical systems are modeled by finite-dimensional sets of ordinary differential equations (ODEs). Others have dynamics that evolve over a continuum (i.e. are infinite-dimensional) and are best modeled by partial differential equations (PDEs), including systems with fluid flows, deformable/flexible structures, or fluid-structure interaction. In practice, PDE models are generally semi-discretized to produce high-fidelity finite-dimensional ODE models. Since the dimension of these models can range from thousands to millions, computational challenges severely limit the use of standard approaches to model-based controller design. In this thesis, we propose an approach for efficiently designing high-performing controllers based on high-dimensional models. Specifically, we develop a model predictive control (MPC) algorithm for solving constrained optimal control problems that leverages high-fidelity, but low-dimensional, reduced order approximations of the original model to satisfy practical computational requirements. In the linear setting, we combine existing ideas from tube MPC with novel approaches for controller synthesis and analysis to develop a reduced order MPC (ROMPC) scheme for solving robust, output feedback control problems, and we provide theoretical closed-loop performance guarantees that explicitly account for model reduction error. We also extend the ROMPC scheme to the nonlinear setting by exploiting piecewise-affine reduced order models. We motivate and validate the proposed approach through two case studies. First, we use a linear, coupled rigid-body/fluid dynamics model for aircraft control, where the high-dimensional computational fluid dynamics (CFD) model has over one million dimensions. Second, we use a nonlinear finite element model (FEM) with over ten thousand dimensions to control a soft robot. Simulation and hardware experiments are used in both studies to demonstrate the practicality and performance of ROMPC.
```
@phdthesis{Lorenzetti2021,
  author = {Lorenzetti, J.},
  title = {Reduced Order Model Predictive Control of High-Dimensional Systems},
  school = {{Stanford University, Dept. of Aeronautics and Astronautics}},
  year = {2021},
  address = {Stanford, California},
  month = aug,
  url = {https://stacks.stanford.edu/file/druid:xb656xk9170/LorenzettiPhD-augmented.pdf},
  owner = {bylard},
  timestamp = {2021-12-06}
}
```
S. Tonkens, J. Lorenzetti, and M. Pavone, “Soft Robot Optimal Control Via Reduced Order Finite Element Models,” in Proc. IEEE Conf. on Robotics and Automation, Xi’an, China, 2021.
[BibTeX] [Abstract]

Abstract: Finite element methods have been successfully used to develop physics-based models of soft robots that capture the nonlinear dynamic behavior induced by continuous deformation. These high-fidelity models are therefore ideal for designing controllers for complex dynamic tasks such as trajectory optimization and trajectory tracking. However, finite element models are also typically very high-dimensional, which makes real-time control challenging. In this work we propose an approach for finite element model-based control of soft robots that leverages model order reduction techniques to significantly increase computational efficiency. In particular, a constrained optimal control problem is formulated based on a nonlinear reduced order finite element model and is solved via sequential convex programming. This approach is demonstrated through simulation of a cable-driven soft robot for a constrained trajectory tracking task, where a 9768-dimensional finite element model is used for controller design.
```
@inproceedings{TonkensLorenzettiEtAl2021,
  author = {Tonkens, S. and Lorenzetti, J. and Pavone, M.},
  title = {Soft Robot Optimal Control Via Reduced Order Finite Element Models},
  booktitle = {{Proc. IEEE Conf. on Robotics and Automation}},
  year = {2021},
  address = {Xi'an, China},
  month = may,
  url = {https://arxiv.org/abs/2011.02092},
  owner = {stonkens},
  timestamp = {2021-06-10}
}
```
J. Lorenzetti and M. Pavone, “Error Bounds for Reduced Order Model Predictive Control,” in Proc. IEEE Conf. on Decision and Control, Jeju Island, Republic of Korea, 2020.
[BibTeX] [Abstract]

Abstract: Model predictive control is a powerful framework for enabling optimal control of constrained systems. However, for systems that are described by high-dimensional state spaces this framework can be too computationally demanding for real-time control. Reduced order model predictive control (ROMPC) frameworks address this issue by leveraging model reduction techniques to compress the state space model used in the online optimal control problem. While this can enable real-time control by decreasing the online computational requirements, these model reductions introduce approximation errors that must be accounted for to guarantee constraint satisfaction and closed-loop stability for the controlled high-dimensional system. In this work we propose an offline methodology for efficiently computing error bounds arising from model reduction, and show how they can be used to guarantee constraint satisfaction in a previously proposed ROMPC framework. This work considers linear, discrete, time-invariant systems that are compressed by Petrov-Galerkin projections, and considers output-feedback settings where the system is also subject to bounded disturbances.
```
@inproceedings{LorenzettiPavone2020b,
  author = {Lorenzetti, J. and Pavone, M.},
  title = {Error Bounds for Reduced Order Model Predictive Control},
  booktitle = {{Proc. IEEE Conf. on Decision and Control}},
  year = {2020},
  address = {Jeju Island, Republic of Korea},
  month = dec,
  url = {https://arxiv.org/pdf/1911.12349.pdf},
  owner = {jlorenze},
  timestamp = {2020-11-30}
}
```
J. Lorenzetti and M. Pavone, “A Simple and Efficient Tube-based Robust Output Feedback Model Predictive Control Scheme,” in European Control Conference, St. Petersburg, Russia, 2020.
[BibTeX] [Abstract]

Abstract: The control of constrained systems using model predictive control (MPC) becomes more challenging when full state information is not available and when the nominal system model and measurements are corrupted by noise. Since these conditions are often seen in practical scenarios, techniques such as robust output feedback MPC have been developed to address them. However, existing approaches to robust output feedback MPC are still challenged by increased complexity of the online optimization problem, increased computational requirements for controller synthesis, or both. In this work we present a simple and efficient methodology for synthesizing a tube-based robust output feedback MPC scheme for linear, discrete, time-invariant systems subject to bounded, additive disturbances. Specifically, we completely avoid the use of Minkowski addition during controller synthesis and the online optimization problem has the same complexity as in the nominal full state feedback MPC problem, enabling our approach to scale with system dimension more effectively than previously proposed schemes.
```
@inproceedings{LorenzettiPavone2020,
  author = {Lorenzetti, J. and Pavone, M.},
  title = {A Simple and Efficient Tube-based Robust Output Feedback Model Predictive Control Scheme},
  booktitle = {{European Control Conference}},
  year = {2020},
  address = {St. Petersburg, Russia},
  month = may,
  url = {https://arxiv.org/pdf/1911.07360.pdf},
  owner = {jlorenze},
  timestamp = {2020-08-03}
}
```
A. McClellan, J. Lorenzetti, M. Pavone, and C. Farhat, “Projection-based Model Order Reduction for Flight Dynamics and Model Predictive Control,” in AIAA Scitech Forum, Orlando, Florida, 2020.
[BibTeX] [Abstract]

Abstract: A model predictive control algorithm seeks to produce a control law that optimizes the future behavior of a deployed system over a finite time horizon, by leveraging a real-time computational model of this system. For applications involving fluid-structure interaction (FSI), this leveraging is challenging because it implies the design of an accurate and yet real-time computational model for the prediction of the time-dependent flow-induced forces and moments acting on the system. The projection-based reduction of CFD-based computational models for FSI provides one approach for addressing this issue. In this context, linear model reduction is adequate as the controller can be expected to maintain the system of interest within small perturbations around a pre-designed optimal trajectory. For the automated landing of an aircraft application considered in this paper, this requires the construction of a CFD-based projection-based reduced-order model that is linearized around a time-dependent trajectory rather than a mere steady-state equilibrium position. To this end, a computational approach for the projection-based model order reduction of linearized CFD-based computational models for FSI is presented, with the goal of application to downstream control tasks such as automated aircraft landing. The approach addresses the issues of linearization around a trajectory and construction of stable reduced-order models to achieve real-time computation, while maintaining model accuracy, and thereby enabling model predictive control. It is verified using a simple model predictive control algorithm.
```
@inproceedings{McClellanLorenzettiEtAl2020,
  author = {McClellan, A. and Lorenzetti, J. and Pavone, M. and Farhat, C.},
  title = {Projection-based Model Order Reduction for Flight Dynamics and Model Predictive Control},
  booktitle = {{AIAA Scitech Forum}},
  year = {2020},
  address = {Orlando, Florida},
  month = jan,
  url = {https://arc.aiaa.org/doi/abs/10.2514/6.2020-1190},
  owner = {jlorenze},
  timestamp = {2019-12-02}
}
```
J. Lorenzetti, A. McClellan, C. Farhat, and M. Pavone, “UAV Aircraft Carrier Landing Using CFD-Based Model Predictive Control,” in AIAA Scitech Forum, Orlando, Florida, 2020.
[BibTeX] [Abstract]

Abstract: The control problem associated with autonomous aircraft carrier landings for UAVs is challenging due to requirements on safety, high-performance operation, and uncertain and highly dynamic environments. This work proposes a control scheme for such problems that enables safe operation of the UAV at the limits of its performance by utilizing a model predictive control (MPC) approach. While real-time computation requirements typically limit the fidelity of the models used in optimization-based control, in this work it is demonstrated that high-fidelity computational fluid dynamics (CFD) models can be used within an MPC framework via the construction of a projection-based reduced order model (ROM). An application of a CFD-based MPC scheme to the glideslope tracking problem is then developed to demonstrate the effectiveness of the proposed approach.
```
@inproceedings{LorenzettiMcClellanEtAl2020,
  author = {Lorenzetti, J. and McClellan, A. and Farhat, C. and Pavone, M.},
  title = {{UAV} Aircraft Carrier Landing Using {CFD}-Based Model Predictive Control},
  booktitle = {{AIAA Scitech Forum}},
  year = {2020},
  address = {Orlando, Florida},
  month = jan,
  url = {/wp-content/papercite-data/pdf/Lorenzetti.McClellan.Farhat.Pavone.AIAA20.pdf},
  owner = {jlorenze},
  timestamp = {2019-12-02}
}
```
B. Landry, J. Lorenzetti, Z. Manchester, and M. Pavone, “Bilevel Optimization for Planning through Contact: A Semidirect Method,” in Int. Symp. on Robotics Research, Hanoi, Vietnam, 2019.
[BibTeX] [Abstract]

Abstract: Many robotics applications, from object manipulation to locomotion, require planning methods that are capable of handling the dynamics of contact. Trajectory optimization has been shown to be a viable approach that can be made to support contact dynamics. However, the current state-of-the art methods remain slow and are often difficult to get to converge. In this work, we leverage recent advances in bilevel optimization to design an algorithm capable of efficiently generating trajectories that involve making and breaking contact. We demonstrate our method’s efficiency by outperforming an alternative state-of-the-art method on a benchmark problem. We moreover demonstrate the method’s ability to design a simple periodic gait for a quadruped with 15 degrees of freedom and four contact points
```
@inproceedings{LandryLorenzettiEtAl2019,
  author = {Landry, B. and Lorenzetti, J. and Manchester, Z. and Pavone, M.},
  title = {Bilevel Optimization for Planning through Contact: A Semidirect Method},
  booktitle = {{Int. Symp. on Robotics Research}},
  year = {2019},
  address = {Hanoi, Vietnam},
  month = oct,
  url = {https://arxiv.org/pdf/1906.04292.pdf},
  owner = {blandry},
  timestamp = {2020-04-13}
}
```
J. Lorenzetti, B. Landry, S. Singh, and M. Pavone, “Reduced Order Model Predictive Control For Setpoint Tracking,” in European Control Conference, Naples, Italy, 2019.
[BibTeX] [Abstract]

Abstract: Despite the success of model predictive control (MPC), its application to high-dimensional systems, such as flexible structures and coupled fluid/rigid-body systems, remains a largely open challenge due to excessive computational complexity. A promising solution approach is to leverage reduced order models for designing the model predictive controller. In this paper we present a reduced order MPC scheme that enables setpoint tracking while robustly guaranteeing constraint satisfaction for linear, discrete, time-invariant systems. Setpoint tracking is enabled by designing the MPC cost function to account for the steady-state error between the full and reduced order models. Robust constraint satisfaction is accomplished by solving (offline) a set of linear programs to provide bounds on the errors due to bounded disturbances, state estimation, and model approximation. The approach is validated on a synthetic system as well as a high-dimensional linear model of a flexible rod, obtained using finite element methods.
```
@inproceedings{LorenzettiLandryEtAl2019,
  author = {Lorenzetti, J. and Landry, B. and Singh, S. and Pavone, M.},
  title = {Reduced Order Model Predictive Control For Setpoint Tracking},
  booktitle = {{European Control Conference}},
  year = {2019},
  address = {Naples, Italy},
  month = jun,
  url = {https://arxiv.org/pdf/1811.06590.pdf},
  owner = {jlorenze},
  timestamp = {2019-04-26}
}
```
J. Lorenzetti, M. Chen, B. Landry, and M. Pavone, “Reach-Avoid Games Via Mixed-Integer Second-Order Cone Programming,” in Proc. IEEE Conf. on Decision and Control, Miami Beach, Florida, 2018.
[BibTeX] [Abstract]

Abstract: Reach-avoid games are excellent proxies for studying many problems in robotics and related fields, with applications including multi-robot systems, human-robot interactions, and safety-critical systems. Solving reach-avoid games is however difficult due to the conflicting and asymmetric goals of agents, and trade-offs between optimality, computational complexity, and solution generality are commonly required. This paper seeks to find attacker strategies in reach-avoid games that reduce computational complexity while retaining solution quality by using a receding horizon strategy. To solve for the open-loop strategy fast enough to enable an receding horizon approach, the problem is formulated as a mixed-integer second-order cone program. This formulation leverages the use of sums-of-squares optimization to provide guarantees that the strategy is robust to all possible defender policies. The method is demonstrated through numerical and hardware experiments.
```
@inproceedings{LorenzettiChenEtAl2018,
  author = {Lorenzetti, J. and Chen, M. and Landry, B. and Pavone, M.},
  title = {Reach-Avoid Games Via Mixed-Integer Second-Order Cone Programming},
  booktitle = {{Proc. IEEE Conf. on Decision and Control}},
  year = {2018},
  address = {Miami Beach, Florida},
  month = dec,
  url = {/wp-content/papercite-data/pdf/Lorenzetti.Chen.Landry.Pavone.CDC18.pdf},
  owner = {jlorenze},
  timestamp = {2019-09-25}
}
```

Contacts:

Joseph Lorenzetti

Awards:

ASL Publications