## Real-time Trajectory Planning for Ground and Aerial Vehicles in a Dynamic EnvironmentIn this dissertation, a novel and generic solution of trajectory generation is developed and evaluated for ground and aerial vehicles in a dynamic environment. By explicitly considering a kinematic model of the ground vehicles, the family of feasible trajectories and their corresponding steering controls are derived in a closed form and are expressed in terms of one adjustable parameter for the purpose of collision avoidance. A collision-avoidance condition is developed for the dynamically changing environment, which consists of a time criterion and a geometrical criterion. By imposing this condition, one can determine a family of collision-free paths in a closed form. Then, optimization problems with respect to different performance indices are setup to obtain optimal solutions from the feasible trajectories. Among these solutions, one with respect to the near-shortest distance and another with respect to the near-minimal control energy are analytical and simple. These properties make them good choices for real-time trajectory planning. Such optimal paths meet all boundary conditions, are twice differentiable, and can be updated in real time once a change in the environment is detected. Then this novel method is extended to 3D space to find a real-time optimal path for aerial vehicles. After that, to reflect the real applications, obstacles are classified to two types: "hard" obstacles that must be avoided, and "soft" obstacles that can be run over/through. Moreover, without losing generality, avoidance criteria are extended to obstacles with any geometric shapes. This dissertation also points out that the emphases of the future work are to consider other constraints such as the bounded velocity and so on. The proposed method is illustrated by computer simulations. |

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### Contents

REVIEW OF PLANNING | 7 |

REALTIME TRAJECTORY PLANNING FOR GROUND | 24 |

REALTIME TRAJECTORY PLANNING FOR AERIAL | 55 |

TRAJECTORY PLANNING FOR GROUND VEHICLES WITH | 83 |

### Common terms and phrases

3D space analytical solution angular velocity body angle boundary conditions C-space car-like mobile vehicle car-like vehicle CCA,B cell decomposition methods chained form chapter collision avoidance criterion collision-free interval collision-free trajectories computation computation space convex polygonal deﬁned diﬀerent dynamic environment dynamically changing environment dynamically moving eﬀectively equation family of trajectories ﬁgure ﬁnd ﬁrst ﬁxed ﬂying vehicle goal graph hard initial straight line iteration ith obstacle kinematic constraints kinematic model L2 norm line segments minimal control energy motion planning moving obstacles near-minimal control energy near-shortest nonholonomic nonholonomic systems optimal feasible trajectory optimal solution optimal trajectory optimization problem order polynomial parabola path of vehicle path planning performance index potential ﬁeld methods radius real-time trajectory planning relative velocity sampling period satisﬁes sensor range shortest path shown in Figure simple arcs soft solved steering theorem trajectory obtained vehicle’s vertexes visibility graph voronoi diagram waypoints