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

该资助将为自主系统（例如移动的机器人和自动驾驶汽车）的控制和轨迹优化问题提供新的理论和算法，预计将对国民经济的各个方面产生重大的积极影响，从自动驾驶汽车和机器人的货物灵活运输到提高制造业的生产力和效率。这项研究将创建算法和系统方法来计算候选轨迹或路径的集合，这些候选轨迹或路径将自动系统转移到相应的目的地集合，而不是计算到单个目的地的单个轨迹或路径。具有多个备选路径和对应的目的地为用户提供了显著的灵活性。后一点与关于使用汽车导航系统的日常经验一致，汽车导航系统通常提供具有不同时间和交通状况的替代路线，而不是单一路线。轨迹生成问题中的这种范式转变是由以下事实激发的：在实践中，用户难以准确地预测系统将操作的未来条件（例如，天气和交通状况），因此，致力于单一轨迹可能不是理想的。这类问题的主要瓶颈之一是实时处理不确定性（例如，天气条件的变化可能会使某些候选轨迹比其他轨迹更不适合）。研究团队将创建易于处理的基于模型和数据驱动的算法，这些算法可以实时执行，而不会影响处理不确定性的能力。最后，将通过一系列研究和教学活动鼓励本科生和代表性不足的学生参与。该研究还将对其他类型的控制问题产生影响，包括计算神经科学和医学以及随机神经系统。这项研究工作将为基于模型和数据驱动的随机最优控制方法的不确定动力系统创建可扩展和实时可实现的轨迹生成算法。在这项研究中，边界条件对应的概率分布，而不是固定的状态。这类随机轨迹生成问题承认在最一般的情况下，一个无限维的表示，这是计算上难以处理的。这项研究依赖于有限维表示，其中的不确定性是显式使用随机微分方程的框架或间接使用广义多项式混沌理论。将开发两种表示的变分积分器，以实现真实的时间优化，并提供对离散化误差的鲁棒性。这项研究还将创建数据驱动（即，无模型）轨迹优化算法，其中系统的不确定状态的前两个时刻的时间演化根据机器学习方法来描述（即，高斯过程），其利用沿着系统的后续轨迹沿着收集的数据。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.