Special Seminar | Joint MechE/IDSS Networked Systems and Connection Science
Title: A Mathematical Theory of Co-Design
Abstract: Everything comes together in the field of robotics. The design of a robotic system involves the choice of actuators, the choice of sensors, the choice of the energy source, the choice of the computation substrate, the choice of the representations, the choice of the algorithms (perception, planning, and control). The irreducible complexity of robotics comes from the fact that the feasibility of the design depends on recursive “co-design constraints” among all those heterogenous domains. Currently, the design of robotic systems is an “art”; as the complexity of robotic systems increases, we will need to transition from relying on expert craftsmanship to systematic theory and tools for design.
I will describe a mathematical “theory of co-design” that is able to capture the irreducible complexity of robotics, and might be useful for other domains involving systems of comparable complexity. The objects of this theory are “design problems”, described as feasibility relations between “functionality provided” and “resources used”. The basic property studied is a monotonicity property, which is: if the required functionality is increased, the required resources do not decrease. This property is intrinsic, in the sense that is invariant to any order-preserving reparameterization. I will show that this family of “Monotone Co-Design Problems” (MCDPs) is closed to composition operations through operations that are the equivalent of series, parallel, and feedback interconnection.
The queries that can be answered based on these models are of the form “minimize resources, subject to minimal functionality provided” or, dually, “maximize functionality, subject to maximum resources usage”. I will show that assuming Scott-continuity (a property stronger than monotonicity, but much weaker than topological continuity) is sufficient to allow a systematic solution procedure that finds the set of all non-dominating solutions based on the elementary theory of fixed points on partially ordered sets (Kleene/Tarski). The complexity depends on the richness of the functionality/resources spaces (measured by height and width of their posets), as well as the structure of the co-design graph.
I will also describe a formal language for describing MCDPs as well as a prototype interpreter/solver. Open-source software is available at http://mcdp.mit.edu/.
Bio: Andrea Censi is a research scientist and principal investigator with the Laboratory of Information and Decision Systems at MIT. He received a Ph.D. from the California Institute of Technology in Control & Dynamical Systems. Currently, he is also Chief Technology Officer of Duckietown Engineering co., an MIT-affiliated startup developing a fleet of autonomous vehicles.