Our goal is to develop and implement numerical methods and optimization algorithms that can generate provably safe and optimal trajectories for multiple vehicle missions in real time, and that account for the presence of environmental uncertainties. The framework is general to encompass most multi-agent system missions. We are particularly interested in the formulation and approximation of infinite-dimensional stochastic optimal control problems into discrete deterministic optimization problems, with provable constraint satisfaction guarantees and convergence properties.
The approach that we plan to undertake builds upon the use of direct approximation methods based on Bernstein polynomials [1]-[5]. The algorithm relies on computationally inexpensive geometric and polynomial methods, and it is shown to be particularly suitable for multiple vehicle missions since it allows efficient enforcement of inter-vehicle collision avoidance constraints, guaranteeing safety at low computational cost. The projected work addresses new challenges in the areas of optimal control in the presence of uncertainty. To meet the goal of producing real time solutions, polynomial chaos techniques are employed. To further improve the computational speed, machine learning methods will be leveraged to further approximate the problem. While machine learning approaches can produce results quickly, they cannot guarantee safety constraints. By joining numerical methods with machine learning, results can be computed quickly while retaining the desired property of ensuring safety constraints.
Bebot
We are currently developing BeBOT, a python toolkit for the use of Bernstein polynomials for trajectory generation. The toolkit is available on our github website. The figures below illustrate examples where BeBOT is used to generate trajectories for multiple vehicles.
[1] V. Cichella, I. Kaminer, C. Walton, and N. Hovakimyan. Optimal motion planning for differentially flat systems using Bernstein approximation. IEEE Control Systems Letters, 2(1):181–186, 2018. Link
[2] V. Cichella, I. Kaminer, C. Walton, N. Hovakimyan, and A. Pascoal. Bernstein approximation of optimal control problems. arXiv preprint arXiv:1812.06132, 2018.
[3] C. Kielas-Jensen, V. Cichella. Trajectory Generation Toolkit for Multiple Autonomous Vehicles Using Bernstein Polynomials. International Conference on Intelligent Robots and Systems (IROS). November 4-8, 2019.
[4] V. Cichella, I. Kaminer, C. Walton, N. Hovakimyan, A. M. Pascoal. Consistent Approximation of Optimal Control Problems using Bernstein Polynomials. In Proceedings of the 58th IEEE Conference on Decision and Control (CDC). 2019.
[5] V. Cichella, I. Kaminer, C. Walton, N. Hovakimyan, and A. M. Pascoal. Optimal Multi-Vehicle Motion Planning using Bernstein Approximants. Transactions on Automatic Control. 2019. Under review.