Collision Avoidance Techniques And Optimal Synthesis For Motion Planning Applications

This dissertation focuses on the problem of motion planning for autonomous agents that are required to perform fast and reactive maneuvers. In realistic situations, this problem needs to be solved in real-time for environments that are both dynamic and partially known. The success of the provided motion plans also relies on the agent’s ability to accurately perform the prescribed maneuvers and, as such, consideration of the input constraints is often times necessary. The problem can be posed in two different ways: as a controllability problem, where trajectory generation is only concerned with satisfying the given boundary conditions, system constraints (dynamic and input constraints) and state constraints (forbidden areas in the state space); or as an optimal control problem, where the trajectory is also required to optimize some performance measure. The main contributions of this dissertation are two-fold. First, a new numerical technique is proposed for solving time-optimal control problems for an agent moving in a spatiotemporal drift field. The solution technique computes the minimum time function and the corresponding time-optimal feedback control law, while using an extremal front expansion procedure to filter out sub-optimal solutions. This methodology can be applied for a rich class of time-optimal control problems where the control input structure is determined by a parameter family of differential equations. To demonstrate its applicability, the numerical technique is implemented for the Zermelo navigation problem on a sphere and for the steering problem of a self-propelled particle in a flow field. Next, in the second part of this dissertation, the controllability problem in the presence of obstacles can be solved using local reactive collision avoidance vector fields. The proposed approach uses the concept of local parametrized guidance vector fields that are generated directly from the agent model and encode collision avoidance behaviors. Their generation relies on a decomposition of agent kinematics and on a proximity-based velocity modulation determined by specific eigenvalue functions. Further exploiting the modulation properties arising from the nature of these eigenvalue functions, curvature constraints can be guaranteed. Closed-form steering laws are determined in accordance with the computed collision avoidance vector fields and can provide the necessary avoidance maneuvers to guarantee problem feasibility. Throughout this dissertation, examples and simulation results in different types of environments are presented and discussed. In the final part of this dissertation, the motion planning problem is tackled for more complex environments. The two proposed methodologies for optimal control and for collision avoidance are combined to yield a hybrid controller that generates near-optimal feasible plans in the presence of multiple static and moving obstacles and of spatiotemporal drift fields