Substantial improvements in artificial intelligence, computing resources, and software tools have enabled tremendous capabilities to mobile robots and autonomous systems. The problem of navigation is a core topic in robotics and autonomous vehicles, as the majority of robotic applications require safe path planning and obstacle avoidance (Yang et al., 2018). Ideally, a solution to this problem considers collision-free navigation in dynamic environments, computationally affordable algorithms for real-time implementation, and optimal control strategies. Such a challenging problem should be addressed in the continuous-time domain, as naive discretization of the system dynamics and the policy space, disregards critical information and leads to discretization errors (Lillicrap et al., 2015). In addition, dynamic environments impose time constraints to the motion planning problem, because collision-free navigation is only ensured for limited time frames (Nägeli et al., 2017). The latter necessitates a finite-horizon formulation to the optimal control problem. Moreover, system modeling is a challenging task with inevitable model simplifications and inaccuracies (Berkenkamp and Schoellig, 2015). Thus, a combination of optimal and adaptive control is needed. Finally, even if the system dynamics are assumed to be known, the finite-horizon optimal control problem requires extensive offline computations to solve the Hamilton-Jacobi-Bellman equation (Lewis et al., 2012).

Our aim in this work is to present a real-time kinodynamic motion planning technique for dynamic environments with unpredictably appearing obstacles. We address the finite-horizon optimal control problem with completely unknown system dynamics. The unknown model is considered to be continuous-time linear time-invariant.

Motion planning in high-dimensions has been addressed with probabilistic road-maps (PRM) (Kavraki et al., 1996) and rapidly-exploring random trees (RRT) (Kuffner and LaValle, 2000; LaValle, 1998). These algorithms are probabilistically complete, but not optimal. The work of Karaman and Frazzoli (2011) proposed a variation of RRT based on rewiring, namely RRT*. The latter was proved to be probabilistically complete and asymptotically optimal. These methods do not incorporate realistic system dynamics and instead use...