Autonomous mobile robots—both aerial and terrestrial vehicles—have gained immense importance due to the broad spectrum of their potential military and civilian applications. One of the indispensable requirements for the autonomy of a mobile vehicle is the vehicle’s capability of planning and executing its motion, that is, finding appropriate control inputs for the vehicle such that the resulting vehicle motion satisfies the requirements of the vehicular task. The motion planning and control problem is inherently complex because it involves two disparate sub-problems: (1) satisfaction of the vehicular task requirements, which requires tools from combinatorics and/or formal methods, and (2) design of the vehicle control laws, which requires tools from dynamical systems and control theory.

Accordingly, this problem is usually decomposed and solved over two levels of hierarchy. The higher level, called the geometric path planning level, finds a geometric path that satisfies the vehicular task requirements, e.g., obstacle avoidance. The lower level, called the trajectory planning level, involves sufficient smoothening of this geometric path followed by a suitable time parametrization to obtain a reference trajectory for the vehicle.

Although simple and efficient, such hierarchical decomposition suffers a serious drawback: the geometric path planner has no information of the kinematical and dynamical constraints of the vehicle. Consequently, the geometric planner may produce paths that the trajectory planner cannot transform into a feasible reference trajectory. Two main ideas appear in the literature to remedy this problem: (a) randomized sampling-based planning, which eliminates the geometric planner altogether by planning in the vehicle state space, and (b) geometric planning supported by feedback control laws. The former class of methods suffer from a lack of optimality of the resultant trajectory, while the latter class of methods makes a restrictive assumption concerning the vehicle kinematical model.

We propose a hierarchical motion planning framework based on a novel mode of interaction between these two levels of planning. This interaction rests on the solution of a special shortest-path problem on graphs, namely, one using costs defined on multiple edge transitions in the path instead of the usual single edge transition costs. These costs are provided by a local trajectory generation algorithm, which we implement using model predictive control and the concept of effective target sets for simplifying the non-convex constraints involved in the problem. The proposed motion planner ensures “consistency” between the two levels of planning, i.e., a guarantee that the higher level geometric path is always associated with a kinematically and dynamically feasible trajectory.

The main contributions of this thesis are: 1. A motion planning framework based on history-dependent costs (H-costs) in cell decomposition graphs for incorporating vehicle dynamical constraints: this framework offers distinct advantages in comparison with the competing approaches of discretization of the state space, of randomized sampling-based motion planning, and of local feedback-based, decoupled hierarchical motion planning, 2. An efficient and flexible algorithm for finding optimal H-cost paths, 3. A precise and general formulation of a local trajectory problem (the tile motion planning problem) that allows independent development of the discrete planner and the trajectory planner, while maintaining “compatibility” between the two planners, 4. A local trajectory generation algorithm using mpc, and the application of the concept of effective target sets for a significant simplification of the local trajectory generation problem, 5. The geometric analysis of curvature-bounded traversal of rectangular channels, leading to less conservative results in comparison with a result reported in the literature, and also to the efficient construction of effective target sets for the solution of the tile motion planning problem, 6. A wavelet-based multi-resolution path planning scheme, and a proof of completeness of the proposed scheme: such proofs are altogether absent from other works on multi-resolution path planning, 7. A technique for extracting all information about cells—namely, the locations, the sizes, and the associated image intensities—directly from the set of significant detail coefficients considered for path planning at a given iteration, and 8. The extension of the multi-resolution path planning scheme to include vehicle dynamical constraints using the aforementioned history-dependent costs approach.

The future work includes an implementation of the proposed framework involving a discrete planner that solves classical planning problems more general than the single-query path planning problem considered thus far, and involving trajectory generation schemes for realistic vehicle dynamical models such as the bicycle model.