When designing autonomous systems, we need to consider multiple trade-offs at various abstraction levels, and the choices of single (hardware and software) components need to be studied jointly.
In this work we consider the problem of designing the control algorithm as well as the platform on which it is executed.
In particular, we focus on vehicle control systems, and formalize state-of-the-art control schemes as monotone feasibility relations.
We then show how, leveraging a monotone theory of co-design, we can study the embedding of control synthesis problems into the task-driven co-design problem of a robotic platform.
The properties of the proposed approach are illustrated by considering urban driving scenarios.
We show how, given a particular task, we can efficiently compute Pareto optimal design solutions.
@article{ZardiniTask22,
title={Task-driven Modular Co-design of Vehicle Control Systems},
author={Zardini, Gioele and Suter, Zelio and Censi, Andrea and Frazzoli, Emilio},
year={2022}
}
Categorification of Negative Information using Enrichment
(M) A. Censi, E. Frazzoli, J. Lorand, G. Zardini
5th Annual International Applied Category Theory Conference, Strathclyde (UK), 2022
Electronic Proceedings in Theoretical Computer Science (EPTCS)
In many applications of category theory it is useful to reason about “negative information”.
For example, in planning problems, providing an optimal solution is the same as giving a feasible solution (the “positive” information) together with a proof of the fact that there cannot be feasible solutions better than the one given (the “negative” information).
We model negative information by introducing the concept of “norphisms”, as opposed to the positive information of morphisms.
A “nategory” is a category that has “Nom”-sets in addition to hom-sets, and specifies the compatibility rules between norphisms and morphisms.
With this setup we can choose to work in “coherent” “subnategories”: subcategories that describe a potential instantiation of the world in which all morphisms and norphisms are compatible.
We derive the composition rules for norphisms in a coherent subnategory; we show that norphisms do not compose by themselves, but rather they need to use morphisms as catalysts.
We have two distinct rules of the type morphism+norphism→norphism.
We then show that those complex rules for norphism inference are actually as natural as the ones for morphisms, from the perspective of enriched category theory.
Every small category is enriched over P = ⟨Set, ×, 1⟩. We show that we can derive the machinery of norphisms by considering an enrichment over a certain monoidal category called PN (for “positive”/“negative”). In summary, we show that an alternative to considering negative information using logic on top of the categorical formalization is to “categorify” the negative information, obtaining negative arrows that live at the same level as the positive arrows, and suggest that the new inference rules are born of the same substance from the perspective of enriched category theory.
@article{zarACT2022,
title={Categorification of Negative Information using Enrichment},
author={Censi, Andrea and Frazzoli, Emilio and Lorand, Jonathan and Zardini, Gioele},
year={2022}
booktitle = {{\rm Proceedings of the 5th Annual International}
Applied Category Theory Conference 2022,
series = {Electronic Proceedings in Theoretical Computer Science},
publisher = {Open Publishing Association},
}
The design of future mobility solutions (autonomous vehicles, micromobility solutions, etc.) and the design of the mobility systems they enable
are closely coupled. Indeed, knowledge about the intended service of novel mobility solutions would impact their design and deployment process,
whilst insights about their technological development could significantly affect transportation management policies. This requires tools to study
such a coupling and co-design future mobility systems in terms of different objectives. This paper presents a framework to address such co-design
problems. In particular, we leverage the recently developed mathematical theory of co-design to frame and solve the problem of designing and
deploying an intermodal mobility system, whereby autonomous vehicles service travel demands jointly with micromobility solutions such as shared
bikes and e- scooters, and public transit, in terms of fleets sizing, vehicle char- acteristics, and public transit service frequency.
Our framework is modular and compositional, allowing one to describe the design problem as the interconnection of its individual components and
to tackle it from a system-level perspective. Moreover, it only requires very general monotonicity assumptions and it naturally handles multiple
objectives, delivering the rational solutions on the Pareto front and thus enabling policy makers to select a policy. To showcase our methodology,
we present a real- world case study for Washington D.C., USA. Our work suggests that it is possible to create user-friendly optimization tools
to systematically assess the costs and benefits of interventions, and that such analytical techniques might inform policy-making in the future.
@article{zardini2022camod,
title={Co-Design to Enable User-Friendly Tools to Assess the Impact of Future Mobility Solutions},
author={Zardini, Gioele and Lanzetti, Nicolas and Censi, Andrea and Frazzoli, Emilio and Pavone, Marco},
journal={IEEE Transactions on Network Science and Engineering},
year={2022}
}
Challenged by urbanization and increasing travel needs, existing transportation systems call for new mobility paradigms.
In this article, we present the emerging concept of Autonomous Mobility-on-Demand, whereby centrally orchestrated fleets of autonomous vehicles provide mobility service to customers.
We provide a comprehensive review of methods and tools to model and solve problems related to Autonomous Mobility-on-Demand systems.
Specifically, we first identify problem settings for their analysis and control, both from the operational and the planning perspective.
We then review modeling aspects, including transportation networks, transportation demand, congestion, operational constraints, and interactions with existing infrastructure.
Thereafter, we provide a systematic analysis of existing solution methods and performance metrics, highlighting trends and trade-offs.
Finally, we present various directions for further research.
@article{zardiniAnnRev2021,
title={Analysis and Control of Autonomous Mobility-on-Demand Systems: A Review},
author={Zardini, Gioele and Lanzetti, Nicolas and Pavone, Marco and Frazzoli, Emilio},
journal={Annual Review of Control, Robotics, and Autonomous Systems},
volume = {5},
year={2022},
doi = {10.1146/annurev-control-042920-012811},
}
Modern applications require robots to comply with multiple, often conflicting rules and to interact with the other agents.
We present Posetal Games as a class of games in which each player expresses a preference over the outcomes via a partially ordered set of metrics.
This allows one to combine hierarchical priorities of each player with the interactive nature of the environment.
By contextualizing standard game theoretical notions, we provide two sufficient conditions on the preference of the players to prove existence of pure Nash Equilibria in finite action sets.
Moreover, we define formal operations on the preference structures and link them to a refinement of the game solutions, showing how the set of equilibria can be systematically shrunk.
The presented results are showcased in a driving game where autonomous vehicles select from a finite set of trajectories.
The results demonstrate the interpretability of results in terms of minimum-rank-violation for each player.
@article{zzral22,
title={Posetal Games: Efficiency, Existence, and Refinement of Equilibria in Games with Prioritized Metrics},
author={Zanardi, Alessandro and Zardini, Gioele and Srinivasan, Bolognani and Bolognani, Saverio and Censi, Andrea and Dörfler, Florian and Frazzoli, Emilio},
journal={IEEE Robotics and Automation Letters},
year={2022},
volume={7},
number={2},
pages={1292-1299},
doi={10.1109/LRA.2021.3135030}
}
2021
Co-Design of Embodied Intelligence: A Structured Approach G. Zardini, D. Milojevic, A. Censi, E. Frazzoli
Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Prague (Czech Republic), 2021
We consider the problem of formally co-designing embodied intelligence as a whole, from hardware components such as chassis and sensors
to software modules such as control and perception pipelines. We propose a principled approach to formulate and solve complex embodied
intelligence co- design problems, leveraging a monotone co-design theory. The methods we propose are intuitive and integrate
heterogeneous engineering disciplines, allowing analytical and simulation- based modeling techniques and enabling interdisciplinarity.
We illustrate through a case study how, given a set of desired behaviors, our framework is able to compute Pareto efficient solutions
for the entire hardware and software stack of a self- driving vehicle.
@article{zardini2021formal,
title={Co-Design of Embodied Intelligence: A Structured Approach},
author={Zardini, Gioele and Milojevic, Dejan and Censi, Andrea and Frazzoli, Emilio},
booktitle={2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)},
year={2021}
volume={},
number={},
pages={7536-7543},
doi={10.1109/IROS51168.2021.9636513}
}
Game Theory to Study Interactions between Mobility Stakeholders G. Zardini*, N. Lanzetti*, L. Guerrini, E. Frazzoli, F. Dörfler
Proceedings of the IEEE 24th International Conference on Intelligent Transportation Systems (ITSC), Indianapolis, Indiana (USA), 2021 Best Paper Award (1st Place)
Increasing urbanization and exacerbation of sustainability goals threaten the operational efficiency of current transportation systems and confront cities
with complex choices with huge impact on future generations. At the same time, the rise of private, profit-maximizing Mobility Service Providers leveraging
public resources, such as ride-hailing companies, entangles current regulation schemes. This calls for tools to study such complex socio-technical problems.
In this paper, we provide a game-theoretic framework to study interactions between stakeholders of the mobility ecosystem, modeling regulatory aspects such
as taxes and public transport prices, as well as operational matters for Mobility Service Providers such as pricing strategy, fleet sizing, and vehicle design.
Our framework is modular and can readily accommodate different types of Mobility Service Providers, actions of municipalities, and low-level models of customers
choices in the mobility system. Through both an analytical and a numerical case study for the city of Berlin, Germany, we showcase the ability of our framework
to compute equilibria of the problem, to study fundamental tradeoffs, and to inform stakeholders and policy makers on the effects of interventions.
Among others, we show tradeoffs between customers satisfaction, environmental impact, and public revenue, as well as the impact of strategic decisions
on these metrics.
@article{zardinilanzetti2021,
title={Game Theory to Study Interactions between Mobility Stakeholders},
author={Zardini, Gioele and Lanzetti, Nicolas and Guerrini, Laura and Frazzoli, Emilio and Dörfler, Florian},
booktitle={2021 IEEE International Intelligent Transportation Systems Conference (ITSC)},
year={2021}
volume={},
number={},
pages={2054-2061},
doi={10.1109/ITSC48978.2021.9564501}
}
Limits and Colimits in a Category of Lenses
(M) E. Chollet*, B. Clarke*, M. Johnson*, M. Songa*, V. Wang*, G. Zardini*
4th Annual International Applied Category Theory Conference, Cambridge (UK), 2021
Electronic Proceedings in Theoretical Computer Science (EPTCS) Paper award - Distinguished keynote talk
Lenses are an important tool in applied category theory.
While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown.
In this paper, we study the category of small categories and asymmetric delta lenses, and prove that it has several good exactness properties.
These properties include the existence of certain limits and colimits, as well as so-called imported limits, such as imported products and imported pullbacks, which have arisen previously in applications.
The category is also shown to be extensive, and it has an image factorisation system.
@article{zarACT2021,
title={Limits and Colimits in a Category of Lenses},
author={Chollet, Emma and Clarke, Bryce and Johnson, Michael and Songa, Maurine and Wang, Vincent and Zardini, Gioele},
booktitle = {{\rm Proceedings of the Fourth International Conference on}
Applied Category Theory,
{\rm Cambridge, United Kingdom, 12-16th July 2021}},
editor = {Kishida, Kohei},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {372},
publisher = {Open Publishing Association},
pages = {164-177},
doi = {10.4204/EPTCS.372.12},
year={2022}
}
Designing cyber-physical systems is a complex task which requires insights at multiple abstraction levels. The choices of single
components are deeply interconnected and need to be jointly studied. In this work, we consider the problem of co-designing the
control algorithm as well as the platform around it. In particular, we leverage a monotone theory of co- design to formalize
variations of the LQG control problem as monotone feasibility relations. We then show how this enables the embedding of control
co-design problems in the higher level co-design problem of a robotic platform. We illustrate the properties of our formalization
by analyzing the co-design of an autonomous drone performing search-and-rescue tasks and show how, given a set of desired robot
behaviors, we can compute Pareto efficient design solutions.
@inproceedings{zardini2020co,
title={Co-Design of Autonomous Systems: From Hardware Selection to Control Synthesis},
author={Zardini, Gioele and Censi, Andrea and Frazzoli, Emilio},
booktitle={2021 European Control Conference (ECC)},
year={2021},
volume={},
number={},
pages={682-689},
doi={10.23919/ECC54610.2021.9654960}
}
2020
On the Co-Design of AV-Enabled Mobility Systems G. Zardini, N. Lanzetti, M. Salazar, A. Censi, E. Frazzoli, M. Pavone
Proceedings of the IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC), Rhodes (Greece), 2020
The design of autonomous vehicles (AVs) and the design of AV-enabled mobility systems are closely coupled. Indeed, knowledge
about the intended service of AVs would impact their design and deployment process, whilst insights about their technological
development could significantly affect transportation management decisions. This calls for tools to study such a coupling and
co-design AVs and AV-enabled mobility systems in terms of different objectives. In this paper, we instantiate a framework to
address such co-design problems. In particular, we leverage the recently developed theory of co-design to frame and solve the
problem of designing and deploying an intermodal Autonomous Mobility-on-Demand system, whereby AVs service travel demands
jointly with public transit, in terms of fleet sizing, vehicle autonomy, and public transit service frequency.
Our framework is modular and compositional, allowing one to describe the design problem as the interconnection of its
individual components and to tackle it from a system-level perspective. To showcase our methodology, we present a
real-world case study for Washington D.C., USA. Our work suggests that it is possible to create user-friendly optimization
tools to systematically assess costs and benefits of interventions, and that such analytical techniques might gain a momentous
role in policy-making in the future.
@inproceedings{ZardiniEtAl2020,
author = {Zardini, G. and Lanzetti, N. and Salazar, M. and Censi, A. and Frazzoli, E. and Pavone, M.},
title = {On the Co-Design of AV-Enabled Mobility Systems},
booktitle={2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC)},
year = {2020},
address = {Rhodes, Greece},
month = sep
doi={10.1109/ITSC45102.2020.9294499}
}
A Compositional Sheaf-Theoretic Framework for Event-Based Systems
(M) G. Zardini, D. I. Spivak, A. Censi, E. Frazzoli
3rd Annual International Applied Category Theory Conference, Cambridge (USA), 2020
Electronic Proceedings in Theoretical Computer Science (EPTCS)
A compositional sheaf-theoretic framework for the modeling of complex event-based systems is presented.
We show that event-based systems are machines, with inputs and outputs, and that they can be composed with machines
of different types, all within a unified, sheaf-theoretic formalism. We take robotic systems as an exemplar of complex systems
and rigorously describe actuators, sensors, and algorithms using this framework.
@Inproceedings{EPTCS333.10,
author = {Zardini, Gioele and Spivak, David I. and Censi, Andrea and Frazzoli, Emilio},
year= {2020},
title = {A Compositional Sheaf-Theoretic Framework for Event-Based Systems},
booktitle = {{\rm Proceedings of the 3rd Annual International}
Applied Category Theory Conference 2020,
{\rm Cambridge, USA, 6-10th July 2020}},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {333},
publisher = {Open Publishing Association},
pages = {139-153},
doi = {10.4204/EPTCS.333.10},
}
The design of Autonomous Vehicles (AVs) and the design of AVs-enabled mobility systems are closely coupled.
Indeed, knowledge about the intended service of AVs would impact their design and deployment process, whilst insights
about their technological development could significantly affect transportation management decisions. This calls for tools
to study such a coupling and co-design AVs and AVs-enabled mobility systems in terms of different objectives. In this paper,
we instantiate a framework to address such co-design problems. In particular, we leverage the recently developed theory of
co-design to frame and solve the problem of designing and deploying an intermodal Autonomous Mobility-on-Demand system, whereby
AVs service travel demands jointly with public transit, in terms of fleet sizing, vehicle autonomy, and public transit service
frequency. Our framework is modular and compositional, allowing to describe the design problem as the interconnection of its
individual components and to tackle it from a system-level perspective. Moreover, it only requires very general monotonicity
assumptions and it naturally handles multiple objectives, delivering the rational solutions on the Pareto front and thus enabling
policy makers to select a solution through “political” criteria. To showcase our methodology, we present a real- world case study
for Washington D.C., USA. Our work suggests that it is possible to create user- friendly optimization tools to systematically
assess the costs and benefits of interventions, and that such analytical techniques might gain a momentous role in policy-making
in the future.
@inproceedings{zardini2020towards,
author = {Zardini, G. and Lanzetti, N. and Salazar, M. and Censi, A. and Frazzoli, E. and Pavone, M.},
title = {Towards a Co-Design Framework for Future Mobility Systems},
booktitle = {99th Annual Meeting of the Transportation Research Board},
year = {2020},
address = {Washington D.C., United States},
month = jan
}
@inproceedings{lanzetti2019self,
title={Do Self-driving Cars Swallow Public Transport? A Game-theoretical Perspective on Transportation Systems},
author={Lanzetti, Nicolas and Zardini, Gioele and Schiffer, Maximilian and Ostrovsky, Michael and Pavone, Marco},
booktitle={INFORMS Annual Meeting 2019},
year={2019}
}
A Co-Design Framework for Future Mobility Systems G. Zardini
Master's Thesis, Autonomous Systems Lab, Stanford University, 2019
Advisors: Dr. Andrea Censi, Prof. Emilio Frazzoli, Prof. Marco Pavone
Towards Task-Driven Closed-Loop Auto-Tuning of Dynamic Vision Sensors G. Zardini
Semester's Thesis, Institute for Dynamic Systems and Control, ETH Zurich, 2018
Advisors: Dr. Jacopo Tani, Prof. Emilio Frazzoli,
An Inductance-Based Sensor for Haptic Feedback Control G. Zardini
Bachelor's Thesis, Multi-Scale Robotics Lab, ETH Zurich, 2017
Advisors: Dr. Georgios Chatzipirpiridis, Prof. Bradley Nelson