Collaborative Research: Real-Time Trajectory Generation Algorithms for Uncertain Autonomous Systems Based on Gaussian Processes

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This grant will contribute new theory and algorithms for control and trajectory optimization problems for autonomous systems, such as mobile robots and autonomous vehicles, which are expected to have a significant positive impact on various aspects of national economy ranging from flexible transportation of goods by self-driving vehicles and robots to increased productivity and efficiency in manufacturing. This research will create algorithms and systematic methods to compute a collection of candidate trajectories or paths that will transfer an autonomous system to a corresponding collection of destinations instead of computing a single trajectory or path to a single destination. Having multiple alternative paths and corresponding destinations provides significant flexibility to the user. The latter point is consistent with every-day experience regarding the use of car navigation systems which often provide alternative routes with different times and traffic conditions in lieu of a single route. This paradigm shift in trajectory generation problems is motivated by the fact that in practice, it is hard for the user to accurately predict the future conditions at which a system will be operating (e.g., weather and traffic conditions) and thus committing to a single trajectory may not be ideal. One of the main bottlenecks in this class of problems is dealing with uncertainty in real-time (for instance, change in weather conditions may render certain candidate trajectories less suitable than others). The research team will create tractable model-based and data-driven algorithms which can be executed in real-time without compromising their ability to handle uncertainty. Finally, participation of undergraduate and underrepresented students will be encouraged through an array of research and teaching activities. The research will also have ramifications to other classes of control problems, including computational neuroscience and medicine and stochastic thermodynamical systems.This research effort will create scalable and real-time implementable trajectory generation algorithms for uncertain dynamical systems based on both model-based and data-driven stochastic optimal control methods. In this research, the boundary conditions correspond to probability distributions rather than fixed states. This class of stochastic trajectory generation problems admits in the most general case an infinite dimensional representation, which is computationally intractable. This research relies instead on finite dimensional representations in which the uncertainty is either represented explicitly using the framework of stochastic differential equations or indirectly by using generalized polynomial chaos theory. Variational integrators for both representations will be developed to achieve real time optimization and provide robustness to discretization errors. This research will also create data-driven (i.e., model-free) trajectory optimization algorithms, in which the time-evolution of the first two moments of the uncertain state of the system is described in terms of machine learning methods (i.e., Gaussian processes) which leverage data collected along the system’s ensuing trajectory. The theory and algorithms of this research will be validated by means of extensive simulations and experiments.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.