Localization and Constrained Non-Linear Optimal Control in Autonomous Systems

Path planning for an autonomous vehicle in a dynamic environment is a challenging problem particularly if the vehicle has to utilize its complete maneuvering abilities, perceive its environment with a high degree of accuracy and react to unsafe conditions. Trajectory planning in an environment with stationary and moving obstacles has been the topic of considerable interest in robotics communities and much of the work focuses on holonomic and non-holonomic kinematics. Optimal path planning has been approached using numerical optimization techniques planning the navigation of ground and aerial navigation producing realistic results in spite of computational complexity. Most of the previous work discussed uses static obstacles and autonomous vehicles moving in closed indoor environments involving prior knowledge of its environment using map based localization and navigation. The work that has focused on dynamic environments with moving obstacles having assumptions of completely known velocities don't account for uncertainty during obstacle motion prediction. Estimation based approaches use grid-based environment representation of the state space, discretized velocities and linear motion models. This simulation aims at finding an optimal trajectory by obtaining the optimal longitudinal and lateral maneuvers using the vehicle's sensing and predictive capabilities for path planning in continuous 2-D space. The focus is on specific scenarios using spatial and temporal constraints while navigating and it involves timed maneuvering in between periods of straight line motion as for a typical unmanned ground vehicle. It also combines tracking obstacles independently and relative localization with targets to achieve its objective. The parametric space of longitudinal and lateral velocities is generated for the host vehicle aiming to reach a goal state configuration within a pre-specified time threshold. This considers independently the cases for completely known trajectories of obstacles and motion under uncertainty. The results of constrained non-linear optimization allow the vehicle to trace its trajectory given its known initial and destination configuration along with known velocity profiles, noise models and range-bearing measurements to the targets in its vicinity. Simulation results show that the proposed scenario-specific approaches produce reasonable maneuvers within the admissible velocity ranges