Trajectory replanning for quadrotors is essential to enable fully autonomous flight in unknown environments. Hierarchical motion planning frameworks, which combine path planning with path parameterization, are popular due to their time efficiency. However, the path planning cannot properly deal with non-static initial states of the quadrotor, which may result in non-smooth or even dynamically infeasible trajectories. In this paper, we present an efficient kinodynamic replanning framework by exploiting the advantageous properties of the B-spline, which facilitates dealing with the non-static state and guarantees safety and dynamical feasibility. Our framework starts with an efficient B-spline-based kinodynamic (EBK) search algorithm which finds a feasible trajectory with minimum control effort and time. To compensate for the discretization induced by the EBK search, an elastic optimization (EO) approach is proposed to refine the control point placement to the optimal location. Systematic comparisons against the state-of-the-art are conducted to validate the performance. Comprehensive onboard experiments using two different vision-based quadrotors are carried out showing the general applicability of the framework.
 In this paper, we present an algorithm for generating complex dynamically feasible maneuvers for autonomous vehicles traveling at high speeds over large distances. Our approach is based on performing anytime incremental search on a multi-resolution, dynamically feasible lattice state space. The resulting planner provides real-time performance and guarantees on and control of the suboptimality of its solution. We provide theoretical properties and experimental results from an implementation on an autonomous passenger vehicle that competed in, and won, the Urban Challenge competition.     We present an online method for generating collision-free trajectories for autonomous quadrotor flight through cluttered environments. We consider the real-world scenario that the quadrotor aerial robot is equipped with limited sensing and operates in initially unknown environments. During flight, an octree-based environment representation is incrementally built using onboard sensors. Utilizing efficient operations in the octree data structure, we are able to generate free-space flight corridors consisting of large overlapping 3-D grids in an online fashion. A novel optimization-based method then generates smooth trajectories that both are bounded entirely within the safe flight corridor and satisfy higher order dynamical constraints. Our method computes valid trajectories within fractions of a second on a moderately fast computer, thus permitting online re-generation of trajectories for reaction to new obstacles. We build a complete quadrotor testbed with onboard sensing, state estimation, mapping, and control, and integrate the proposed method to show online navigation through complex unknown environments. This paper presents LQG-Obstacles, a new concept that combines linear-quadratic feedback control of mobile robots with guaranteed avoidance of collisions with obstacles. Our approach generalizes the concept of Velocity Obstacles [3] to any robotic system with a linear Gaussian dynamics model. We integrate a Kalman filter for state estimation and an LQR feedback controller into a closed-loop dynamics model of which a higher-level control objective is the “control input”. We then define the LQG-Obstacle as the set of control objectives that result in a collision with high probability. Selecting a control objective outside the LQG-Obstacle then produces collision-free motion. We demonstrate the potential of LQG-Obstacles by safely and smoothly navigating a simulated quadrotor helicopter with complex non-linear dynamics and motion and sensing uncertainty through three-dimensional environments with obstacles and narrow passages.   In this work, we propose a search-based planning method to compute dynamically feasible trajectories for a quadrotor flying in an obstacle-cluttered environment. Our approach searches for smooth, minimum-time trajectories by exploring the map using a set of short-duration motion primitives. The primitives are generated by solving an optimal control problem and induce a finite lattice discretization on the state space which can be explored using a graph-search algorithm. The proposed approach is able to generate resolution-complete (i.e., optimal in the discretized space), safe, dynamically feasibility trajectories efficiently by exploiting the explicit solution of a Linear Quadratic Minimum Time problem. It does not assume a hovering initial condition and, hence, is suitable for fast online re-planning while the robot is moving. Quadrotor navigation with online re-planning is demonstrated using the proposed approach in simulation and physical experiments and comparisons with trajectory generation based on state-of-art quadratic programming are presented.   During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the solution obtained by these algorithms, e.g., in terms of a given cost function, have been established so far. The purpose of this paper is to fill this gap, by designing efficient incremental samplingbased algorithms with provable optimality properties. The first contribution of this paper is a negative result: it is proven that, under mild technical conditions, the cost of the best path returned by RRT converges almost surely to a non-optimal value, as the number of samples increases. Second, a new algorithm is considered, called the Rapidly-exploring Random Graph (RRG), and it is shown that the cost of the best path returned by RRG converges to the optimum almost surely. Third, a tree version of RRG is introduced, called RRT∗, which preserves the asymptotic optimality of RRG while maintaining a tree structure like RRT. The analysis of the new algorithms hinges on novel connections between sampling-based motion planning algorithms and the theory of random geometric graphs. In terms of computational complexity, it is shown that the number of simple operations required by both the RRG and RRT∗ algorithms is asymptotically within a constant factor of that required by RRT.  