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This paper presents a method for constructing human-robot interaction policies in settings where multimodality, i.e., the possibility of multiple highly distinct futures, plays a critical role in decision making. We are motivated in this work by the example of traffic weaving, e.g., at highway onramps/offramps, where entering and exiting cars must swap lanes in a short distance — a challenging negotiation even for experienced drivers due to the inherent multimodal uncertainty of who will pass whom. Our approach is to learn multimodal probability distributions over future human actions from a dataset of human-human exemplars and perform real-time robot policy construction in the resulting environment model through massively parallel sampling of human responses to candidate robot action sequences. Direct learning of these distributions is made possible by recent advances in the theory of conditional variational autoencoders (CVAEs), whereby we learn action distributions simultaneously conditioned on the present interaction history, as well as candidate future robot actions in order to take into account response dynamics. We demonstrate the efficacy of this approach with a human-in-the-loop simulation of a traffic weaving scenario.

Human behavior prediction models enable robots to anticipate how humans may react to their actions, and hence are instrumental to devising safe and proactive robot planning algorithms. However, modeling complex interaction dynamics and capturing the possibility of many possible outcomes in such interactive settings is very challenging, which has recently prompted the study of several different approaches. In this work, we provide a self-contained tutorial on a conditional variational autoencoder (CVAE) approach to human behavior prediction which, at its core, can produce a multimodal probability distribution over future human trajectories conditioned on past interactions and candidate robot future actions. Specifically, the goals of this tutorial paper are to review and build a taxonomy of state-of-the-art methods in human behavior prediction, from physics-based to purely data-driven methods, provide a rigorous yet easily accessible description of a data-driven, CVAE-based approach, highlight important design characteristics that make this an attractive model to use in the context of model-based planning for human-robot interactions, and provide important design considerations when using this class of models.

Action anticipation, intent prediction, and proactive behavior are all desirable characteristics for autonomous driving policies in interactive scenarios. Paramount, however, is ensuring safety on the road—a key challenge in doing so is accounting for uncertainty in human driver actions without unduly impacting planner performance. This paper introduces a minimally-interventional safety controller operating within an autonomous vehicle control stack with the role of ensuring collision-free interaction with an externally controlled (e.g., human-driven) counterpart while respecting static obstacles such as a road boundary wall. We leverage reachability analysis to construct a real-time (100Hz) controller that serves the dual role of (1) tracking an input trajectory from a higher-level planning algorithm using model predictive control, and (2) assuring safety through maintaining the availability of a collision-free escape maneuver as a persistent constraint regardless of whatever future actions the other car takes. A full-scale steer-by-wire platform is used to conduct traffic weaving experiments wherein two cars, initially side-by-side, must swap lanes in a limited amount of time and distance, emulating cars merging onto/off of a highway. We demonstrate that, with our control stack, the autonomous vehicle is able to avoid collision even when the other car defies the planner’s expectations and takes dangerous actions, either carelessly or with the intent to collide, and otherwise deviates minimally from the planned trajectory to the extent required to maintain safety.

To achieve seamless human-robot interactions, robots need to intimately reason about complex interaction dynamics and future human behaviors within their motion planning process. However, there is a disconnect between state-of-the-art neural network-based human behavior models and robot motion planners—either the behavior models are limited in their consideration of downstream planning or a simplified behavior model is used to ensure tractability of the planning problem. In this work, we present a framework that fuses together the interpretability and flexibility of trajectory optimization (TO) with the predictive power of state-of-the-art human trajectory prediction models. In particular, we leverage gradient information from data-driven prediction models to explicitly reason about human-robot interaction dynamics within a gradient-based TO problem. We demonstrate the efficacy of our approach in a multi-agent scenario whereby a robot is required to safely and efficiently navigate through a crowd of up to ten pedestrians. We compare against a variety of planning methods, and show that by explicitly accounting for interaction dynamics within the planner, our method offers safer and more efficient behaviors, even yielding proactive and nuanced behaviors such as waiting for a pedestrian to pass before moving.

Humans have a remarkable ability to fluently engage in joint collision avoidance in crowded navigation tasks despite the complexities and uncertainties inherent in human behavior. Underlying these interactions is a mutual understanding that (i) individuals are prosocial, that is, there is equitable responsibility in avoiding collisions, and (ii) individuals should behave legibly, that is, move in a way that clearly conveys their intent to reduce ambiguity in how they intend to avoid others. Toward building robots that can safely and seamlessly interact with humans, we propose a general robot trajectory planning framework for synthesizing legible and proactive behaviors and demonstrate that our robot planner naturally leads to prosocial interactions. Specifically, we introduce the notion of a markup factor to incentivize legible and proactive behaviors and an inconvenience budget constraint to ensure equitable collision avoidance responsibility. We evaluate our approach against well-established multi-agent planning algorithms and show that using our approach produces safe, fluent, and prosocial interactions. We demonstrate the real-time feasibility of our approach with human-in-the-loop simulations.

This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into robotics problems that benefit from gradient-based solutions. Specifically, STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems. The quantitative semantics of STL provide a robustness metric, i.e., how much a signal satisfies or violates an STL specification. In this work, we devise a systematic methodology for translating STL robustness formulas into computation graphs. With this representation, and by leveraging off-the-shelf automatic differentiation tools, we are able to efficiently backpropagate through STL robustness formulas and hence enable a natural and easy-to-use integration of STL specifications with many gradient-based approaches used in robotics. Through a number of examples stemming from various robotics applications, we demonstrate that STLCG is versatile, computationally efficient, and capable of incorporating human-domain knowledge into the problem formulation.

As safety-critical autonomous vehicles (AVs) will soon become pervasive in our society, a number of safety concepts for trusted AV deployment have been recently proposed throughout industry and academia. Yet, agreeing upon an "appropriate" safety concept is still an elusive task. In this paper, we advocate for the use of Hamilton Jacobi (HJ) reachability as a unifying mathematical framework for comparing existing safety concepts, and propose ways to expand its modeling premises in a data-driven fashion. Specifically, we show that (i) existing predominant safety concepts can be embedded in the HJ reachability framework, thereby enabling a common language for comparing and contrasting modeling assumptions, and (ii) HJ reachability can serve as an inductive bias to effectively reason, in a data-driven context, about two critical, yet often overlooked aspects of safety: responsibility and context-dependency.

There are spatio-temporal rules that dictate how robots should operate in complex environments, e.g., road rules govern how (self-driving) vehicles should behave on the road. However, seamlessly incorporating such rules into a robot control policy remains challenging especially for real-time applications. In this work, given a desired spatio-temporal specification expressed in the Signal Temporal Logic (STL) language, we propose a semi-supervised controller synthesis technique that is attuned to human-like behaviors while satisfying desired STL specifications. Offline, we synthesize a trajectory-feedback neural network controller via an adversarial training scheme that summarizes past spatio-temporal behaviors when computing controls, and then online, we perform gradient steps to improve specification satisfaction. Central to the offline phase is an imitation-based regularization component that fosters better policy exploration and helps induce naturalistic human behaviors. Our experiments demonstrate that having imitation-based regularization leads to higher qualitative and quantitative performance compared to optimizing an STL objective only as done in prior work. We demonstrate the efficacy of our approach with an illustrative case study and show that our proposed controller outperforms a state-of-the-art shooting method in both performance and computation time.

Evaluating the safety of an autonomous vehicle (AV) depends on the behavior of surrounding agents which can be heavily influenced by factors such as environmental context and informally-defined driving etiquette. A key challenge is in determining a minimum set of assumptions on what constitutes reasonable foreseeable behaviors of other road users for the development of AV safety models and techniques. In this paper, we propose a data-driven AV safety design methodology that first learns "reasonable" behavioral assumptions from data, and then synthesizes an AV safety concept using these learned behavioral assumptions. We borrow techniques from control theory, namely high order control barrier functions and Hamilton-Jacobi reachability, to provide inductive bias to aid interpretability, verifiability, and tractability of our approach. In our experiments, we learn an AV safety concept using demonstrations collected from a highway traffic-weaving scenario, compare our learned concept to existing baselines, and showcase its efficacy in evaluating real-world driving logs.

Drivers have a responsibility to exercise reasonable care to avoid collision with other road users. This assumed responsibility allows interacting agents to maintain safety without explicit coordination. Thus to enable safe autonomous vehicle (AV) interactions, AVs must understand what their responsibilities are to maintain safety and how they affect the safety of nearby agents. In this work we seek to understand how responsibility is shared in multi-agent settings where an autonomous agent is interacting with human counterparts. We introduce Responsibility-Aware Control Barrier Functions (RA-CBFs) and present a method to learn responsibility allocations from data. By combining safety-critical control and learning-based techniques, RA-CBFs allow us to account for scene-dependent responsibility allocations and synthesize safe and efficient driving behaviors without making worst-case assumptions that typically result in overly-conservative behaviors. We test our framework using real-world driving data and demonstrate its efficacy as a tool for both safe control and forensic analysis of unsafe driving.