This work addresses the problem of coupling vision-based navigation systems for Unmanned Aerial Vehicles (UAVs) with robust obstacle avoidance capabilities. The former is formulated by a maximization of the point of interest visibility, while the latter is modeled by ellipsoidal repulsive areas. The whole problem is transcribed into an Optimal Control Problem (OCP), and solved in a few milliseconds by leveraging state-of-the-art numerical optimization. The resulting trajectories are then well suited to achieve the specified goal location while avoiding obstacles by a safety margin and minimizing the probability to loose track with the target of interest. Combining this technique with a proper ellipsoid shaping (e.g. augmenting the shape with the obstacle velocity, or the obstacle detection uncertainties) results in a robust obstacle avoidance behaviour. We validate our approach within extensive simulated experiments demonstrating (i) capability to satisfy all the constraints, and (ii) the avoidance reactivity even in challenging situations. We release with this paper the open source implementation
An algorithm is proposed allowing for the rapid generation and evaluation of quadrocopter state interception trajectories. These trajectories are from arbitrary initial states to final states defined by the vehicle position, velocity and acceleration with a specified end of time. Sufficient criteria are then derived allowing trajectories to be tested for feasibility with respect to thrust and body rates. It is also shown that the range of a linear combination of the vehicle state can be solved for in closed form, useful e.g. for testing that the position remains within a box. The algorithm is applied by revisiting the problem of finding a trajectory to hit a ball towards a target with a racket attached to a quadrocopter. The trajectory generator is used in a model predictive control like strategy, where thousands of trajectories are generated and evaluated at every controller update step, with the first input of the optimal trajectory being sent to the vehicle. It is shown that the method can generate and evaluate on the order of one million trajectories per second on a standard laptop computer.  This paper addresses the problem of motion planning for fast, agile flight through a dense obstacle field. A key contribution is the design of two families of motion primitives for aerial robots flying in dense obstacle fields, along with rules to stitch them together. The primitives are obtained by solving for the flight dynamics of the aerial robot, and explicitly account for limited agility using time delays. The first family of primitives consists of turning maneuvers to link any two points in space. The locations of the terminal points are used to obtain closed-form expressions for the control inputs required to fly between them, while accounting for the finite time required to switch between consecutive sets of control inputs. The second family consists of aggressive turn-around maneuvers wherein the time delay between the angle of attack and roll angle commands is used to optimize the maneuver for the spatial constraints. A 3-D motion planning algorithm based on these primitives is presented for aircraft flying through a dense forest. 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. Multirotor unmanned aerial vehicles (UAVs) are rapidly gaining popularity for many applications. However, safe operation in partially unknown, unstructured environments remains an open question. In this paper, we present a continuous-time trajectory optimization method for real-time collision avoidance on multirotor UAVs. We then propose a system where this motion planning method is used as a local replanner, that runs at a high rate to continuously recompute safe trajectories as the robot gains information about its environment. We validate our approach by comparing against existing methods and demonstrate the complete system avoiding obstacles on a multirotor UAV platform. The problem of generating a smooth reference path, given a finite family of discrete, locally optimal paths, is investigated. A finite discretization of the environment results in a sequence of obstacle-free square cells. The generated path must lie inside the channel generated by these obstacle-free cells, while minimizing certain performance criteria. Two constrained optimization problems are formulated and solved subject to the given geometric (linear) constraints and boundary conditions in order to generate a library of B-spline path templates offline. These templates are recalled during implementation and are merged together on the fly in order to construct a smooth and feasible reference path to be followed by a closed-loop tracking controller. Combined with a discrete path planner, the proposed algorithm provides a complete solution to the obstacle-free path-generation problem for an unmanned aerial vehicle in a computationally efficient manner, which is suitable for real-time implementation.