Game-theoretic models are effective tools for modeling multi-agent interactions, especially when robots need to coordinate with humans. However, applying these models requires inferring their specifications from observed behaviors—a challenging task known as the inverse game problem. Existing inverse game approaches often struggle to account for behavioral uncertainty and measurement noise, and leverage both offline and online data. To address these limitations, we propose an inverse game method that integrates a generative trajectory model into a differentiable mixed-strategy game framework. By representing the mixed strategy with a conditional variational autoencoder (CVAE), our method can infer high-dimensional, multi-modal behavior distributions from noisy measurements while adapting in real-time to new observations. We extensively evaluate our method in a simulated navigation benchmark, where the observations are generated by an unknown game model. Despite the model mismatch, our method can infer Nash-optimal actions comparable to those of the ground-truth model and the oracle inverse game baseline, even in the presence of uncertain agent objectives and noisy measurements.

A major challenge to deploying robots widely is navigation in human-populated environments, commonly referred to as social robot navigation . While the field of social navigation has advanced tremendously in recent years, the fair evaluation of algorithms that tackle social navigation remains hard because it involves not just robotic agents moving in static environments but also dynamic human agents and their perceptions of the appropriateness of robot behavior. In contrast, clear, repeatable, and accessible benchmarks have accelerated progress in fields like computer vision, natural language processing and traditional robot navigation by enabling researchers to fairly compare algorithms, revealing limitations of existing solutions and illuminating promising new directions. We believe the same approach can benefit social navigation. In this article, we pave the road toward common, widely accessible, and repeatable benchmarking criteria to evaluate social robot navigation. Our contributions include (a) a definition of a socially navigating robot as one that respects the principles of safety, comfort, legibility, politeness, social competency, agent understanding, proactivity, and responsiveness to context, (b) guidelines for the use of metrics, development of scenarios, benchmarks, datasets, and simulators to evaluate social navigation, and (c) a design of a social navigation metrics framework to make it easier to compare results from different simulators, robots, and datasets.

Ergodic search enables optimal exploration of an information distribution with guaranteed asymptotic coverage of the search space. However, current methods typically have exponential computational complexity and are limited to Euclidean space. We introduce a computationally efficient ergodic search method. Our contributions are two-fold as follows: First, we develop a kernel-based ergodic metric, generalizing it from Euclidean space to Lie groups. We prove this metric is consistent with the exact ergodic metric and ensures linear complexity. Second, we derive an iterative optimal control algorithm for trajectory optimization with the kernel metric. Numerical benchmarks show our method is two orders of magnitude faster than the state-of-the-art method. Finally, we demonstrate the proposed algorithm with a peg-in-hole insertion task. We formulate the problem as a coverage task in the space of SE(3) and use a 30-s-long human demonstration as the prior distribution for ergodic coverage. Ergodicity guarantees the asymptotic solution of the peg-in-hole problem so long as the solution resides within the prior information distribution, which is seen in the 100% success rate.

Robot navigation in crowded public spaces is a complex task that requires addressing a variety of engineering and human factors challenges. These challenges have motivated a great amount of research resulting in important developments for the fields of robotics and human-robot interaction over the past three decades. Despite the significant progress and the massive recent interest, we observe a number of significant remaining challenges that prohibit the seamless deployment of autonomous robots in crowded environments. In this survey article, we organize existing challenges into a set of categories related to broader open problems in robot planning, behavior design, and evaluation methodologies. Within these categories, we review past work and offer directions for future research. Our work builds upon and extends earlier survey efforts by (a) taking a critical perspective and diagnosing fundamental limitations of adopted practices in the field and (b) offering constructive feedback and ideas that could inspire research in the field over the coming decade.

Real-time navigation in dense human environments is a challenging problem in robotics. Most existing path planners fail to account for the dynamics of pedestrians because introducing time as an additional dimension in search space is computationally prohibitive. Alternatively, most local motion planners only address imminent collision avoidance and fail to offer long-term optimality. In this work, we present an approach, called Dynamic Channels, to solve this global to local quandary. Our method combines the high-level topological path planning with low-level motion planning into a complete pipeline. By formulating the path planning problem as graph-searching in the triangulation space, our planner is able to explicitly reason about the obstacle dynamics and capture the environmental change efficiently. We evaluate efficiency and performance of our approach on public pedestrian datasets and compare it to a state-of-the-art planning algorithm for dynamic obstacle avoidance. Completeness proofs are provided in the supplement at http://caochao.me/files/proof.pdf. An extended version of the paper is available on arXiv.

Independent mobility is important for the self-esteem and well-being of people with mobility impairments. For people with severe disabilities, there is a body of research investigating how best to share control of motion between a person with disabilities and a "smart wheelchair". Traditionally in "shared control", the control law is a linear combination of the human's intended velocity and the path planner's velocity. However, this formulation of sharing control between a human and a machine does not guarantee safety on a theoretical level. To guarantee safety in formulating the blending of the human's input velocity and planner's velocity, we implement a practical form of probabilistic shared control formulated by Trautman. We tested this shared control by conducting experiments in a simulation where participants drive a wheelchair. The results of the experiment suggest probabilistic shared control has similar performance to linear blending in terms of significant reduction in number of collisions. However, for the sip-puff switch (a particularly difficult interface to use), probabilistic shared control yielded a greater reduction in collisions than linear blending.

We explore the probabilistic foundations of shared control in complex dynamic environments. In order to do this, we formulate shared control as a random process and describe the joint distribution that governs its behavior. For tractability, we model the relationships between the operator, autonomy, and crowd as an undirected graphical model. Further, we introduce an interaction function between the operator and the robot, that we call "agreeability", in combination with the methods developed in [26], we extend a cooperative collision avoidance autonomy to shared control. We therefore quantify the notion of simultaneously optimizing over agreeability (between the operator and autonomy), and safety and efficiency in crowded environments. We show that for a particular form of interaction function between the autonomy and the operator, linear blending is recovered exactly. Additionally, to recover linear blending, unimodal restrictions must be placed on the models describing the operator and the autonomy. In turn, these restrictions raise questions about the flexibility and applicability of the linear blending framework. Additionally, we present an extension of linear blending called "operator biased linear trajectory blending" (which formalizes some recent approaches in linear blending such as [10]) and show that not only is this also a restrictive special case of our probabilistic approach, but more importantly, is statistically unsound, and thus, mathematically, unsuitable for implementation. Instead, we suggest a statistically principled approach that guarantees data is used in a consistent manner, and show how this alternative approach converges to the full probabilistic framework. We conclude by proving that, in general, linear blending is suboptimal with respect to the joint metric of agreeability, safety, and efficiency.

We consider mobile robot navigation in dense human crowds. In particular, we explore two questions. Can we design a navigation algorithm that encourages humans to cooperate with a robot? Would such cooperation improve navigation performance? We address the first question by developing a probabilistic predictive model of cooperative collision avoidance and goal-oriented behavior by extending the interacting Gaussian processes approach to include multiple goals and stochastic movement duration. We answer the second question with an extensive quantitative study of robot navigation in dense human crowds (488 runs completed), specifically testing how cooperation models effect navigation performance. We find that the “multiple goal” interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities near 1 person/m2, while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as this multiple goal extension, and more than twice as often as the basic interacting Gaussian processes. Furthermore, a reactive planner based on the widely used “dynamic window” approach fails for crowd densities above 0.55 people/m2. Based on these experimental results, and previous theoretical observations, we conclude that a cooperation model is important for safe and efficient robot navigation in dense human crowds.

In this paper, we study the safe navigation of a mobile robot through crowds of dynamic agents with uncertain trajectories. Existing algorithms suffer from the “freezing robot” problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused on reducing the predictive uncertainty for individual agents by employing more informed models or heuristically limiting the predictive covariance to prevent this overcautious behavior. In this work, we demonstrate that both the individual prediction and the predictive uncertainty have little to do with the frozen robot problem. Our key insight is that dynamic agents solve the frozen robot problem by engaging in “joint collision avoidance”: They cooperatively make room to create feasible trajectories. We develop IGP, a nonparametric statistical model based on dependent output Gaussian processes that can estimate crowd interaction from data. Our model naturally captures the non-Markov nature of agent trajectories, as well as their goal-driven navigation. We then show how planning in this model can be efficiently implemented using particle based inference. Lastly, we evaluate our model on a dataset of pedestrians entering and leaving a building, first comparing the model with actual pedestrians, and find that the algorithm either outperforms human pedestrians or performs very similarly to the pedestrians. We also present an experiment where a covariance reduction method results in highly overcautious behavior, while our model performs desirably.