  Although dynamic games provide a rich paradigm for modeling agents'
interactions, solving these games for real-world applications is often
challenging. Many real-world interactive settings involve general nonlinear
state and input constraints that couple agents' decisions with one another. In
this work, we develop an efficient and fast planner for interactive trajectory
optimization in constrained setups using a constrained game-theoretical
framework. Our key insight is to leverage the special structure of agents'
objective and constraint functions that are common in multi-agent interactions
for fast and reliable planning. More precisely, we identify the structure of
agents' cost and constraint functions under which the resulting dynamic game is
an instance of a constrained dynamic potential game. Constrained dynamic
potential games are a class of games for which instead of solving a set of
coupled constrained optimal control problems, a constrained Nash equilibrium,
i.e. a Generalized Nash equilibrium, can be found by solving a single
constrained optimal control problem. This simplifies constrained interactive
trajectory optimization significantly. We compare the performance of our method
in a navigation setup involving four planar agents and show that our method is
on average 20 times faster than the state-of-the-art. We further provide
experimental validation of our proposed method in a navigation setup involving
two quadrotors carrying a rigid object while avoiding collisions with two
humans.
