Towards a Trajectory Planning Concept: Augmenting Path Planning Methods by Considering Speed Limit Constraints

Trajectory planning is an essential part of systems controlling autonomous entities such as vehicles or robots. It requires not only finding spatial curves but also that dynamic properties of the vehicles (such as speed limits for certain maneuvers) must be followed. In this paper, we present an approach for augmenting existing path planning methods to support basic dynamic constraints, concretely speed limit constraints. We apply this approach to the well known A* and state-of-the-art Theta* and Lazy Theta* path planning algorithms. We use a concept of trajectory planning based on a modular architecture in which spatial and dynamic parts can be easily implemented. This concept allows dynamic aspects to be processed during planning. Existing systems based on a similar concept usually add dynamics (velocity) into spatial curves in a post-processing step which might be inappropriate when the curves do not follow the dynamics. Many existing trajectory planning approaches, especially in mobile robotics, encode dynamic aspects directly in the representation (e.g. in the form of regular lattices) which requires a precise knowledge of the environmental and dynamic properties of particular autonomous entities making designing and implementing such trajectory planning approaches quite difficult. The concept of trajectory planning we implemented might not be as precise but the modular architecture makes the design and implementation easier because we can use (modified) well known path planning methods and define models of dynamics of autonomous entities separately. This seems to be appropriate for simulations used in feasibility studies for some complex autonomous systems or in computer games etc. Our basic implementation of the augmented A*, Theta* and Lazy Theta* algorithms is also experimentally evaluated. We compare i) the augmented and basic A*, Theta* and Lazy Theta* algorithms and ii) optimizing of augmented Theta* and Lazy Theta* for distance (the trajectory length) and duration (time needed to move through the trajectory.