Mark J. Debord

Matthew R. Kirchner, Mark J. Debord, João P. Hespanha

We present a method for optimal coordination of multiple vehicle teams when multiple endpoint configurations are equally desirable, such as seen in the autonomous assembly of formation flight. The individual vehicles' positions in the formation are not assigned a priori and a key challenge is to find the optimal configuration assignment along with the optimal control and trajectory. Commonly, assignment and trajectory planning problems are solved separately. We introduce a new multi-vehicle coordination paradigm, where the optimal goal assignment and optimal vehicle trajectories are found simultaneously from a viscosity solution of a single Hamilton-Jacobi (HJ) partial differential equation (PDE), which provides a necessary and sufficient condition for global optimality. Intrinsic in this approach is that individual vehicle dynamic models need not be the same, and therefore can be applied to heterogeneous systems. Numerical methods to solve the HJ equation have historically relied on a discrete grid of the solution space and exhibits exponential scaling with system dimension, preventing their applicability to multiple vehicle systems. By utilizing a generalization of the Hopf formula, we avoid the use of grids and present a method that exhibits polynomial scaling in the number of vehicles.

Alex Tong Lin, Mark J. Debord, Katia Estabridis et al.

We consider a multi-agent reinforcement learning problem where each agent seeks to maximize a shared reward while interacting with other agents, and they may or may not be able to communicate. Typically the agents do not have access to other agent policies and thus each agent is situated in a non-stationary and partially-observable environment. In order to obtain multi-agents that act in a decentralized manner, we introduce a novel algorithm under the popular framework of centralized training, but decentralized execution. This training framework first obtains solutions to a multi-agent problem with a single centralized joint-space learner, which is then used to guide imitation learning for independent decentralized multi-agents. This framework has the flexibility to use any reinforcement learning algorithm to obtain the expert as well as any imitation learning algorithm to obtain the decentralized agents. This is in contrast to other multi-agent learning algorithms that, for example, can require more specific structures. We present some theoretical bounds for our method, and we show that one can obtain decentralized solutions to a multi-agent problem through imitation learning.