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 @math agents and @math step lookahead, @math 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 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 space---and propose a novel solution: optimize over trajectory 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 .
@cite_39: We present PROCAB, an efficient method for Probabilistically Reasoning from Observed Context-Aware Behavior. It models the context-dependent utilities and underlying reasons that people take different actions. The model generalizes to unseen situations and scales to incorporate rich contextual information. We train our model using the route preferences of 25 taxi drivers demonstrated in over 100,000 miles of collected data, and demonstrate the performance of our model by inferring: (1) decision at next intersection, (2) route to known destination, and (3) destination given partially traveled route.
@cite_19: Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior is an approximately optimal solution to an unknown decision problem. These techniques learn a utility function that explains the example behavior and can then be used to accurately predict or imitate future behavior in similar observed or unobserved situations. In this work, we consider similar tasks in competitive and cooperative multi-agent domains. Here, unlike single-agent settings, a player cannot myopically maximize its reward; it must speculate on how the other agents may act to influence the game's outcome. Employing the game-theoretic notion of regret and the principle of maximum entropy, we introduce a technique for predicting and generalizing behavior.
@cite_49: We present a novel approach for determining robot movements that efficiently accomplish the robot's tasks while not hindering the movements of people within the environment. Our approach models the goal-directed trajectories of pedestrians using maximum entropy inverse optimal control. The advantage of this modeling approach is the generality of its learned cost function to changes in the environment and to entirely different environments. We employ the predictions of this model of pedestrian trajectories in a novel incremental planner and quantitatively show the improvement in hindrance-sensitive robot trajectory planning provided by our approach.
@cite_58: The goal of this research is to enable mobile robots to navigate through crowded environments such as indoor shopping malls, airports, or downtown side walks. The key research question addressed in this paper is how to learn planners that generate human-like motion behavior. Our approach uses inverse reinforcement learning (IRL) to learn human-like navigation behavior based on example paths. Since robots have only limited sensing, we extend existing IRL methods to the case of partially observable environments. We demonstrate the capabilities of our approach using a realistic crowd flow simulator in which we modeled multiple scenarios in crowded environments. We show that our planner learned to guide the robot along the flow of people when the environment is crowded, and along the shortest path if no people are around.
@cite_11: The ability to act in a socially-aware way is a key skill for robots that share a space with humans. In this paper we address the problem of socially-aware navigation among people that meets objective criteria such as travel time or path length as well as subjective criteria such as social comfort. Opposed to model-based approaches typically taken in related work, we pose the problem as an unsupervised learning problem. We learn a set of dynamic motion prototypes from observations of relative motion behavior of humans found in publicly available surveillance data sets. The learned motion prototypes are then used to compute dynamic cost maps for path planning using an any-angle A* algorithm. In the evaluation we demonstrate that the learned behaviors are better in reproducing human relative motion in both criteria than a Proxemics-based baseline method.
Some approaches learn navigation strategies by observing example trajectories. @cite_11 , learned motion prototypes guide navigation. @cite_39 , maximum entropy inverse reinforcement learning (max-Ent IRL) learns taxi cab driver navigation strategies from data; this method is extended to an office navigation robot in @cite_49 . @cite_58 , max-Ent IRL is extended to dynamic environments. Their planner is trained using trajectories, and the method recovers a planner which duplicates the behavior of the simulator. @cite_19 , agents how to act in multi-agent settings using game theory and the principle of maximum entropy.