Papers & talks

(2020) “An overview to monotone co-design theory”.

2020 talk at MIT Categories Seminar .

(2015) “Monotone Co-Design Problems: or, everything is the same”.

Co-design with categories

Co-design is explained in Chapter 4 of “Seven Sketches in Compositionality” by Spivak and Fong.

Co-design Applications

Gioele Zardini, Nicolas Lanzetti, Andrea Censi, Emilio Frazzoli, Marco Pavone. Co-Design to Enable User-Friendly Tools to Assess the Impact of Future Mobility Solutions. Preprint, 2020. pdf supp. materialbibtex

@article{zardini2020co,
        author = "Zardini, Gioele and Lanzetti, Nicolas and Censi, Andrea and Frazzoli, Emilio and Pavone, Marco",
        title = "Co-Design to Enable User-Friendly Tools to Assess the Impact of Future Mobility Solutions",
        url = "https://arxiv.org/abs/2008.08975",
        year = "2020",
        pdf = "https://arxiv.org/pdf/2008.08975.pdf",
        institution = "ETH Zurich"
    }

This paper applies a monotone theory of co-design to model and solve the co-design of future mobility systems. In particular, we show how such a formalism allows for a user-friendly framework, which allows stakeholders to assess the impact of future mobility solutions, such as autonomous vehicles and micrmobility.

Gioele Zardini, Dejan Milojevic, Andrea Censi, Emilio Frazzoli. A Formal Approach to the Co-Design of Embodied Intelligence. Preprint, 2020. pdf supp. materialbibtex

@article{zardini2020formal,
        author = "Zardini, Gioele and Milojevic, Dejan and Censi, Andrea and Frazzoli, Emilio",
        title = "A Formal Approach to the Co-Design of Embodied Intelligence",
        url = "https://arxiv.org/abs/2011.10756",
        year = "2020",
        pdf = "https://arxiv.org/pdf/2011.10756",
        institution = "ETH Zurich"
    }

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.

Co-design without categories

This paper is currently the best reference for the algorithmics:

Andrea Censi. A mathematical theory of co-design. Technical Report, Laboratory for Information and Decision Systems, MIT, September 2016. pdf supp. materialbibtex

@techreport{censi16codesign,
        author = "Censi, Andrea",
        title = "A Mathematical Theory of Co-Design",
        url = "https://arxiv.org/abs/1512.08055",
        month = "September",
        year = "2016",
        pdf = "https://arxiv.org/pdf/1512.08055",
        institution = "Laboratory for Information and Decision Systems, MIT"
    }

This paper introduces a theory of co-design that describes "design problems", defined as tuples of "functionality space", "implementation space", and "resources space", together with a feasibility relation that relates the three spaces. Design problems can be interconnected together to create "co-design problems", which describe possibly recursive co-design constraints among subsystems.

This is a rather technical paper with more examples and the description of the certainty handling mechanism currently implemented:

Andrea Censi. Uncertainty in monotone co-design problems. Robotics and Automation Letters, 2017. pdf supp. materialbibtex

@article{censi17uncertainty,
        author = "Censi, Andrea",
        title = "Uncertainty in Monotone Co-Design Problems",
        url = "https://arxiv.org/abs/1609.03103",
        journal = "Robotics and Automation Letters",
        year = "2017",
        pdf = "https://arxiv.org/pdf/1609.03103",
        institution = "Laboratory for Information and Decision Systems, MIT"
    }

This paper concerns the introduction of uncertainty in the MCDP framework. Uncertainty has two roles: first, it allows to deal with limited knowledge in the models; second, it also can be used to generate consistent relaxations of a problem, as the computation requirements can be lowered should the user accept some uncertainty in the answer.