Andrea Censi

Alessandro Zanardi, Pier Giuseppe Sessa, Nando Käslin et al.

We consider the interaction among agents engaging in a driving task and we model it as general-sum game. This class of games exhibits a plurality of different equilibria posing the issue of equilibrium selection. While selecting the most efficient equilibrium (in term of social cost) is often impractical from a computational standpoint, in this work we study the (in)efficiency of any equilibrium players might agree to play. More specifically, we bound the equilibrium inefficiency by modeling driving games as particular type of congestion games over spatio-temporal resources. We obtain novel guarantees that refine existing bounds on the Price of Anarchy (PoA) as a function of problem-dependent game parameters. For instance, the relative trade-off between proximity costs and personal objectives such as comfort and progress. Although the obtained guarantees concern open-loop trajectories, we observe efficient equilibria even when agents employ closed-loop policies trained via decentralized multi-agent reinforcement learning.

Alessandro Zanardi, Andrea Censi, Margherita Atzei et al.

Autonomous Vehicles (AVs) promise a range of societal advantages, including broader access to mobility, reduced road accidents, and enhanced transportation efficiency. However, evaluating the risks linked to AVs is complex due to limited historical data and the swift progression of technology. This paper presents a data-driven framework for assessing the risk of different AVs' behaviors in various operational design domains (ODDs), based on counterfactual simulations of "misbehaving" road users. We propose the notion of counterfactual safety margin, which represents the minimum deviation from nominal behavior that could cause a collision. This methodology not only pinpoints the most critical scenarios but also quantifies the (relative) risk's frequency and severity concerning AVs. Importantly, we show that our approach is applicable even when the AV's behavioral policy remains undisclosed, through worst- and best-case analyses, benefiting external entities like regulators and risk evaluators. Our experimental outcomes demonstrate the correlation between the safety margin, the quality of the driving policy, and the ODD, shedding light on the relative risks of different AV providers. Overall, this work contributes to the safety assessment of AVs and addresses legislative and insurance concerns surrounding this burgeoning technology.

Alessandro Zanardi, Pietro Zullo, Andrea Censi et al.

Modern robotics often involves multiple embodied agents operating within a shared environment. Path planning in these cases is considerably more challenging than in single-agent scenarios. Although standard Sampling-based Algorithms (SBAs) can be used to search for solutions in the robots' joint space, this approach quickly becomes computationally intractable as the number of agents increases. To address this issue, we integrate the concept of factorization into sampling-based algorithms, which requires only minimal modifications to existing methods. During the search for a solution we can decouple (i.e., factorize) different subsets of agents into independent lower-dimensional search spaces once we certify that their future solutions will be independent of each other using a factorization heuristic. Consequently, we progressively construct a lean hypergraph where certain (hyper-)edges split the agents to independent subgraphs. In the best case, this approach can reduce the growth in dimensionality of the search space from exponential to linear in the number of agents. On average, fewer samples are needed to find high-quality solutions while preserving the optimality, completeness, and anytime properties of SBAs. We present a general implementation of a factorized SBA, derive an analytical gain in terms of sample complexity for PRM*, and showcase empirical results for RRG.

Dejan Milojevic, Gioele Zardini, Miriam Elser et al.

This paper discusses the integration challenges and strategies for designing mobile robots, by focusing on the task-driven, optimal selection of hardware and software to balance safety, efficiency, and minimal usage of resources such as costs, energy, computational requirements, and weight. We emphasize the interplay between perception and motion planning in decision-making by introducing the concept of occupancy queries to quantify the perception requirements for sampling-based motion planners. Sensor and algorithm performance are evaluated using False Negative Rates (FPR) and False Positive Rates (FPR) across various factors such as geometric relationships, object properties, sensor resolution, and environmental conditions. By integrating perception requirements with perception performance, an Integer Linear Programming (ILP) approach is proposed for efficient sensor and algorithm selection and placement. This forms the basis for a co-design optimization that includes the robot body, motion planner, perception pipeline, and computing unit. We refer to this framework for solving the co-design problem of mobile robots as CODEI, short for Co-design of Embodied Intelligence. A case study on developing an Autonomous Vehicle (AV) for urban scenarios provides actionable information for designers, and shows that complex tasks escalate resource demands, with task performance affecting choices of the autonomy stack. The study demonstrates that resource prioritization influences sensor choice: cameras are preferred for cost-effective and lightweight designs, while lidar sensors are chosen for better energy and computational efficiency.

Alessandro Zanardi, Gioele Zardini, Sirish Srinivasan et al.

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.

Anthony Courchesne, Andrea Censi, Liam Paull

In many situations it is either impossible or impractical to develop and evaluate agents entirely on the target domain on which they will be deployed. This is particularly true in robotics, where doing experiments on hardware is much more arduous than in simulation. This has become arguably more so in the case of learning-based agents. To this end, considerable recent effort has been devoted to developing increasingly realistic and higher fidelity simulators. However, we lack any principled way to evaluate how good a "proxy domain" is, specifically in terms of how useful it is in helping us achieve our end objective of building an agent that performs well in the target domain. In this work, we investigate methods to address this need. We begin by clearly separating two uses of proxy domains that are often conflated: 1) their ability to be a faithful predictor of agent performance and 2) their ability to be a useful tool for learning. In this paper, we attempt to clarify the role of proxy domains and establish new proxy usefulness (PU) metrics to compare the usefulness of different proxy domains. We propose the relative predictive PU to assess the predictive ability of a proxy domain and the learning PU to quantify the usefulness of a proxy as a tool to generate learning data. Furthermore, we argue that the value of a proxy is conditioned on the task that it is being used to help solve. We demonstrate how these new metrics can be used to optimize parameters of the proxy domain for which obtaining ground truth via system identification is not trivial.

Gioele Zardini, David I. Spivak, Andrea Censi et al.

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.

Gioele Zardini, Andrea Censi, Emilio Frazzoli

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.

Gioele Zardini, Dejan Milojevic, Andrea Censi et al.

We consider the problem of co-designing embodied intelligence as a whole in a structured way, from hardware components such as propulsion systems 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.

Jacopo Tani, Andrea F. Daniele, Gianmarco Bernasconi et al.

As robotics matures and increases in complexity, it is more necessary than ever that robot autonomy research be reproducible. Compared to other sciences, there are specific challenges to benchmarking autonomy, such as the complexity of the software stacks, the variability of the hardware and the reliance on data-driven techniques, amongst others. In this paper, we describe a new concept for reproducible robotics research that integrates development and benchmarking, so that reproducibility is obtained "by design" from the beginning of the research/development processes. We first provide the overall conceptual objectives to achieve this goal and then a concrete instance that we have built: the DUCKIENet. One of the central components of this setup is the Duckietown Autolab, a remotely accessible standardized setup that is itself also relatively low-cost and reproducible. When evaluating agents, careful definition of interfaces allows users to choose among local versus remote evaluation using simulation, logs, or remote automated hardware setups. We validate the system by analyzing the repeatability of experiments conducted using the infrastructure and show that there is low variance across different robot hardware and across different remote labs.

Gioele Zardini, David I. Spivak, Andrea Censi et al.

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.

Julian Zilly, Lorenz Hetzel, Andrea Censi et al.

We examine the influence of input data representations on learning complexity. For learning, we posit that each model implicitly uses a candidate model distribution for unexplained variations in the data, its noise model. If the model distribution is not well aligned to the true distribution, then even relevant variations will be treated as noise. Crucially however, the alignment of model and true distribution can be changed, albeit implicitly, by changing data representations. "Better" representations can better align the model to the true distribution, making it easier to approximate the input-output relationship in the data without discarding useful data variations. To quantify this alignment effect of data representations on the difficulty of a learning task, we make use of an existing task complexity score and show its connection to the representation-dependent information coding length of the input. Empirically we extract the necessary statistics from a linear regression approximation and show that these are sufficient to predict relative learning performance outcomes of different data representations and neural network types obtained when utilizing an extensive neural network architecture search. We conclude that to ensure better learning outcomes, representations may need to be tailored to both task and model to align with the implicit distribution of model and task.

Andrea Censi, Saverio Bolognani, Julian G. Zilly et al.

We present a new type of coordination mechanism among multiple agents for the allocation of a finite resource, such as the allocation of time slots for passing an intersection. We consider the setting where we associate one counter to each agent, which we call karma value, and where there is an established mechanism to decide resource allocation based on agents exchanging karma. The idea is that agents might be inclined to pass on using resources today, in exchange for karma, which will make it easier for them to claim the resource use in the future. To understand whether such a system might work robustly, we only design the protocol and not the agents' policies. We take a game-theoretic perspective and compute policies corresponding to Nash equilibria for the game. We find, surprisingly, that the Nash equilibria for a society of self-interested agents are very close in social welfare to a centralized cooperative solution. These results suggest that many resource allocation problems can have a simple, elegant, and robust solution, assuming the availability of a karma accounting mechanism.

Guillermo Gallego, Tobi Delbruck, Garrick Orchard et al.

Event cameras are bio-inspired sensors that differ from conventional frame cameras: Instead of capturing images at a fixed rate, they asynchronously measure per-pixel brightness changes, and output a stream of events that encode the time, location and sign of the brightness changes. Event cameras offer attractive properties compared to traditional cameras: high temporal resolution (in the order of microseconds), very high dynamic range (140 dB vs. 60 dB), low power consumption, and high pixel bandwidth (on the order of kHz) resulting in reduced motion blur. Hence, event cameras have a large potential for robotics and computer vision in challenging scenarios for traditional cameras, such as low-latency, high speed, and high dynamic range. However, novel methods are required to process the unconventional output of these sensors in order to unlock their potential. This paper provides a comprehensive overview of the emerging field of event-based vision, with a focus on the applications and the algorithms developed to unlock the outstanding properties of event cameras. We present event cameras from their working principle, the actual sensors that are available and the tasks that they have been used for, from low-level vision (feature detection and tracking, optic flow, etc.) to high-level vision (reconstruction, segmentation, recognition). We also discuss the techniques developed to process events, including learning-based techniques, as well as specialized processors for these novel sensors, such as spiking neural networks. Additionally, we highlight the challenges that remain to be tackled and the opportunities that lie ahead in the search for a more efficient, bio-inspired way for machines to perceive and interact with the world.

Julian Zilly, Jacopo Tani, Breandan Considine et al.

Despite recent breakthroughs, the ability of deep learning and reinforcement learning to outperform traditional approaches to control physically embodied robotic agents remains largely unproven. To help bridge this gap, we created the 'AI Driving Olympics' (AI-DO), a competition with the objective of evaluating the state of the art in machine learning and artificial intelligence for mobile robotics. Based on the simple and well specified autonomous driving and navigation environment called 'Duckietown', AI-DO includes a series of tasks of increasing complexity -- from simple lane-following to fleet management. For each task, we provide tools for competitors to use in the form of simulators, logs, code templates, baseline implementations and low-cost access to robotic hardware. We evaluate submissions in simulation online, on standardized hardware environments, and finally at the competition event. The first AI-DO, AI-DO 1, occurred at the Neural Information Processing Systems (NeurIPS) conference in December 2018. The results of AI-DO 1 highlight the need for better benchmarks, which are lacking in robotics, as well as improved mechanisms to bridge the gap between simulation and reality.

Andrea Censi, Konstantin Slutsky, Tichakorn Wongpiromsarn et al.

The behavior of self-driving cars must be compatible with an enormous set of conflicting and ambiguous objectives, from law, from ethics, from the local culture, and so on. This paper describes a new way to conveniently define the desired behavior for autonomous agents, which we use on the self-driving cars developed at nuTonomy. We define a "rulebook" as a pre-ordered set of "rules", each akin to a violation metric on the possible outcomes ("realizations"). The rules are partially ordered by priority. The semantics of a rulebook imposes a pre-order on the set of realizations. We study the compositional properties of the rulebooks, and we derive which operations we can allow on the rulebooks to preserve previously-introduced constraints. While we demonstrate the application of these techniques in the self-driving domain, the methods are domain-independent.

Andrea Censi

This work contributes to a compositional theory of "co-design" that allows to optimally design a robotic platform. In this framework, the user describes each subsystem as a monotone relation between "functionality" provided and "resources" required. These models can be easily composed to express the co-design constraints among different subsystems. The user then queries the model, to obtain the design with minimal resources usage, subject to a lower bound on the provided functionality. This paper concerns the introduction of uncertainty in the framework. Uncertainty has two roles: first, it allows to deal with limited knowledge of 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.

Andrea Censi

One of the challenges of modern engineering, and robotics in particular, is designing complex systems, composed of many subsystems, rigorously and with optimality guarantees. 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. A co-design problem induces a family of optimization problems of the type "find the minimal resources needed to implement a given functionality"; the solution is an antichain (Pareto front) of resources. A special class of co-design problems are Monotone Co-Design Problems (MCDPs), for which functionality and resources are complete partial orders and the feasibility relation is monotone and Scott continuous. The induced optimization problems are multi-objective, nonconvex, nondifferentiable, noncontinuous, and not even defined on continuous spaces; yet, there exists a complete solution. The antichain of minimal resources can be characterized as a least fixed point, and it can be computed using Kleene's algorithm. The computation needed to solve a co-design problem can be bounded by a function of a graph property that quantifies the interdependence of the subproblems. These results make us much more optimistic about the problem of designing complex systems in a rigorous way.