Baisravan HomChaudhuri

Abraham P. Vinod, Baisravan Homchaudhuri, Meeko M. K. Oishi

We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure (density) and the forward stochastic reach set. This method is applicable to systems with bounded or unbounded disturbance sets. We also examine the convexity properties of the forward stochastic reach set and its probability density. Motivated by the problem of a robot attempting to capture a stochastically moving, non-adversarial target, we demonstrate our method on two simple examples. Where traditional approaches provide approximations, our method provides exact analytical expressions for the densities and probability of capture.

Baisravan HomChaudhuri, Abraham P. Vinod, Meeko M. K. Oishi

We propose a method to efficiently compute the forward stochastic reach (FSR) set and its probability measure for nonlinear systems with an affine disturbance input, that is stochastic and bounded. This method is applicable to systems with an a priori known controller, or to uncontrolled systems, and often arises in problems in obstacle avoidance in mobile robotics. When used as a constraint in finite horizon controller synthesis, the FSR set, and its probability measure facilitates probabilistic collision avoidance, in contrast to methods which presume the obstacles act in a worst-case fashion and generate hard constraints that cannot be violated. We tailor our approach to accommodate rigid body constraints, and show convexity is assured so long as the rigid body shape of each obstacle is also convex. We extend methods for multi-obstacle avoidance through mixed integer linear programming (with linear robot and obstacle dynamics) to accommodate chance constraints that represent the FSR set probability measure. We demonstrate our method on a rigid-body obstacle avoidance scenario, in which a receding horizon controller is designed to avoid several stochastically moving obstacles while reaching the desired goal. Our approach can provide solutions when approaches that presume a worst-case action from the obstacle fail.

Baisravan HomChaudhuri, Pierluigi Pisu

In this paper, we focus on developing driver-in-the loop fuel economic control strategy for multiple connected vehicles. The control strategy is considered to work in a driver assistance framework where the controller gives command to a driver to follow while considering the ability of the driver in following control commands. Our proposed method uses vehicle-to-vehicle (V2V) communication, exploits traffic lights' Signal Phase and Timing (SPAT) information, models driver error injection with Markov chain, and employs scenario tree based stochastic model predictive control to improve vehicle fuel economy and traffic mobility. The proposed strategy is decentralized in nature as every vehicle evaluates its own strategy using only local information. Simulation results show the effect of consideration of driver error injection when synthesizing fuel economic controllers in a driver assistance fashion.