In this paper, we propose a time-efficient approach to generate safe, smooth and dynamically feasible trajectories for quadrotors in obstacle-cluttered environment. By using the uniform B-spline to represent trajectories, we transform the trajectory planning to a graph-search problem of B-spline control points in discretized space. Highly strict convex hull property of B-spline is derived to guarantee the dynamical feasibility of the entire trajectory. A novel non-uniform kinodynamic search strategy is adopted, and the step length is dynamically adjusted during the search process according to the Euclidean signed distance field (ESDF), making the trajectory achieve reasonable time-allocation and be away from obstacles. Non-static initial and goal states are allowed, therefore it can be used for online local replanning as well as global planning. Extensive simulation and hardware experiments show that our method achieves higher performance comparing with the state-of-the-art method.
In this paper, we propose a framework for online quadrotor motion planning for autonomous navigation in unknown environments. Based on the onboard state estimation and environment perception, we adopt a fast marching-based path searching method to find a path on a velocity field induced by the Euclidean signed distance field (ESDF) of the map, to achieve better time allocation. We generate a flight corridor for the quadrotor to travel through by inflating the path against the environment. We represent the trajectory as piecewise Bezier curves by using Bernstein polynomial basis and formulate the trajectory generation problem as typical convex programs. By using Bezier curves, we are able to bound positions and higher order dynamics of the trajectory entirely within safe regions. The proposed motion planning method is integrated into a customized light-weight quadrotor platform and is validated by presenting fully autonomous navigation in unknown cluttered indoor and outdoor environments. We also release our code for trajectory generation as an open-source package. This paper presents a strategy for improving motion planning of an unmanned helicopter flying in a dense and complex city-like environment. Although Sampling Based Motion planning algorithms have shown success in many robotic problems, problems that exhibit ldquonarrow passagerdquo properties involving kinodynamic planning of high dimensional vehicles like aerial vehicles still present computational challenges. In this work, to solve the kinodynamic motion planning problem of an unmanned helicopter, we suggest a two step planner. In the first step, the planner explores the environment through a randomized reachability tree search using an approximate line segment model. The resulting connecting path is converted into flight way points through a line-of-sight segmentation. In the second step, every consecutive way points are connected with B-Spline curves and these curves are repaired probabilistically to obtain a dynamically feasible path. Numerical simulations in 3D indicate the ability of the method to provide real-time solutions in dense and complex environments. We address the controller design and the trajectory generation for a quadrotor maneuvering in three dimensions in a tightly constrained setting typical of indoor environments. In such settings, it is necessary to allow for significant excursions of the attitude from the hover state and small angle approximations cannot be justified for the roll and pitch. We develop an algorithm that enables the real-time generation of optimal trajectories through a sequence of 3-D positions and yaw angles, while ensuring safe passage through specified corridors and satisfying constraints on velocities, accelerations and inputs. A nonlinear controller ensures the faithful tracking of these trajectories. Experimental results illustrate the application of the method to fast motion (5–10 body lengths second) in three-dimensional slalom courses. We explore the challenges of planning trajectories for quadrotors through cluttered indoor environments. We extend the existing work on polynomial trajectory generation by presenting a method of jointly optimizing polynomial path segments in an unconstrained quadratic program that is numerically stable for high-order polynomials and large numbers of segments, and is easily formulated for efficient sparse computation. We also present a technique for automatically selecting the amount of time allocated to each segment, and hence the quadrotor speeds along the path, as a function of a single parameter determining aggressiveness, subject to actuator constraints. The use of polynomial trajectories, coupled with the differentially flat representation of the quadrotor, eliminates the need for computationally intensive sampling and simulation in the high dimensional state space of the vehicle during motion planning. Our approach generates high-quality trajecrtories much faster than purely sampling-based optimal kinodynamic planning methods, but sacrifices the guarantee of asymptotic convergence to the global optimum that those methods provide. We demonstrate the performance of our algorithm by efficiently generating trajectories through challenging indoor spaces and successfully traversing them at speeds up to 8 m s. A demonstration of our algorithm and flight performance is available at: http: groups.csail.mit.edu rrg quad_polynomial_trajectory_planning. In this paper, we introduce an algorithm for generating collision-free two-lane paths for unmanned vehicles used at mining sites by using quartic (degree 4) B-spline curves. Given the boundary geometry of the haul road area and the positions and orientations of the two-dimensional vehicle at the start and goal points, the algorithm automatically generates a collision-free two-lane path that satisfies the minimum turning radius constraint. Moreover, the resulting path shares the same third derivative at knots (joints), i.e., @math continuity, which guarantees a continuous rate of change of the curvature along the entire path. Examples are provided to demonstrate the effectiveness of the proposed algorithm.