We consider the problem of navigating a mobile robot through dense human crowds. We begin by exploring a fundamental impediment to classical motion planning algorithms called the ''freezing robot problem'': once the environment surpasses a certain level of dynamic complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. We argue that this problem can be avoided if the robot anticipates human cooperation, and accordingly we develop interacting Gaussian processes, a prediction density that captures cooperative collision avoidance, and a ''multiple goal'' extension that models the goal-driven nature of human decision making. We validate this model with an empirical study of robot navigation in dense human crowds (488 runs), specifically testing how cooperation models effect navigation performance. The multiple goal interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities nearing 0.8 humans/m 2 , while a state-of-theart non-cooperative planner exhibits unsafe behavior more than three times as often as the multiple goal extension, and twice as often as the basic interacting Gaussian process approach. Furthermore, a reactive planner based on the widely used dynamic window approach proves insufficient for crowd densities above 0.55 people/m 2 . We also show that our noncooperative planner or our reactive planner capture the salient characteristics of nearly any dynamic navigation algorithm. Based on these experimental results and theoretical observations, we conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.

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 [23], 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 [9]) 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.

Abstract-Some people with severe mobility impairments are unable to operate powered wheelchairs reliably and effectively, using commercially available interfaces. This has sparked a body of research into "smart wheelchairs", which assist users to drive safely and create opportunities for them to use alternative interfaces. Various "shared control" techniques have been proposed to provide an appropriate level of assistance that is satisfactory and acceptable to the user. Most shared control techniques employ a traditional strategy called linear blending (LB), where the user's commands and wheelchair's autonomous commands are combined in some proportion. In this paper, however, we implement a more generalised form of shared control called probabilistic shared control (PSC). This probabilistic formulation improves the accuracy of modelling the interaction between the user and the wheelchair by taking into account uncertainty in the interaction. In this paper, we demonstrate the practical success of PSC over LB in terms of safety, particularly for novice users.

We study the sparsity and optimality properties of crowd navigation and find that existing techniques do not satisfy both criteria simultaneously: either they achieve optimality with a prohibitive number of samples or tractability assumptions make them fragile to catastrophe. For example, if the human and robot are modeled independently, then tractability is attained but the planner is prone to overcautious or overaggressive behavior. For sampling based motion planning of joint human-robot cost functions, for nt agents and T step lookahead, O(2 2n t T ) samples are needed for coverage of the action space. Advanced approaches statically partition the action space into free-space and then sample in those convex regions. However, if the human is moving into free-space, then the partition is misleading and sampling is unsafe: free space will soon be occupied. We diagnose the cause of these deficiencies-optimization happens over trajectory space-and propose a novel solution: optimize over trajectory distribution space by using a Gaussian process (GP) basis. We exploit the "kernel trick" of GPs, where a continuum of trajectories are captured with a mean and covariance function. By using the mean and covariance as proxies for a trajectory family we reason about collective trajectory behavior without resorting to sampling. The GP basis is sparse and optimal with respect to collision avoidance and robot and crowd intention and flexibility. GP sparsity leans heavily on the insight that joint action space decomposes into free regions; however, the decomposition contains feasible solutions only if the partition is dynamically generated. We call our approach O(2 n t )-sparse interacting Gaussian processes.

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 public pedestrian environments. In this survey article, we organize existing challenges into a set of categories related to broader open problems in motion 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 we aspire will drive research in the field over the coming decade.