Real-Time Predictive Modeling and Robust Avoidance of Pedestrians with Uncertain, Changing Intentions

To plan safe trajectories in urban environments, autonomous vehicles must be able to quickly assess the future intentions of dynamic agents. Pedestrians are particularly challenging to model, as their motion patterns are often uncertain and/or unknown a priori. This paper presents a novel changepoint detection and clustering algorithm that, when coupled with offline unsupervised learning of a Gaussian process mixture model (DPGP), enables quick detection of changes in intent and online learning of motion patterns not seen in prior training data. The resulting long-term movement predictions demonstrate improved accuracy relative to offline learning alone, in terms of both intent and trajectory prediction. By embedding these predictions within a chance-constrained motion planner, trajectories which are probabilistically safe to pedestrian motions can be identified in real-time. Hardware experiments demonstrate that this approach can accurately predict pedestrian motion patterns from onboard sensor/perception data and facilitate robust navigation within a dynamic environment.Comment: Submitted to 2014 International Workshop on the Algorithmic Foundations of Robotic

Risk Aversion in Finite Markov Decision Processes Using Total Cost Criteria and Average Value at Risk

In this paper we present an algorithm to compute risk averse policies in Markov Decision Processes (MDP) when the total cost criterion is used together with the average value at risk (AVaR) metric. Risk averse policies are needed when large deviations from the expected behavior may have detrimental effects, and conventional MDP algorithms usually ignore this aspect. We provide conditions for the structure of the underlying MDP ensuring that approximations for the exact problem can be derived and solved efficiently. Our findings are novel inasmuch as average value at risk has not previously been considered in association with the total cost criterion. Our method is demonstrated in a rapid deployment scenario, whereby a robot is tasked with the objective of reaching a target location within a temporal deadline where increased speed is associated with increased probability of failure. We demonstrate that the proposed algorithm not only produces a risk averse policy reducing the probability of exceeding the expected temporal deadline, but also provides the statistical distribution of costs, thus offering a valuable analysis tool

Constrained Risk-Averse Markov Decision Processes

We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures