In order to enable microaerial vehicles (MAVs) to assist in complex, unknown, unstructured environments, they must be able to navigate with guaranteed safety, even when faced with a cluttered environment they have no prior knowledge of. While trajectory-optimization-based local planners have been shown to perform well in these cases, prior work either does not address how to deal with local minima in the optimization problem or solves it by using an optimistic global planner. We present a conservative trajectory-optimization-based local planner, coupled with a local exploration strategy that selects intermediate goals. We perform extensive simulations to show that this system performs better than the standard approach of using an optimistic global planner and also outperforms doing a single exploration step when the local planner is stuck. The method is validated through experiments in a variety of highly cluttered environments including a dense forest. These experiments show the complete system running in real time fully onboard an MAV, mapping and replanning at 4 Hz.
With the increased use of high degree-of-freedom robots that must perform tasks in real-time, there is a need for fast algorithms for motion planning. In this work, we view motion planning from a probabilistic perspective. We consider smooth continuous-time trajectories as samples from a Gaussian process (GP) and formulate the planning problem as probabilistic inference. We use factor graphs and numerical optimization to perform inference quickly, and we show how GP interpolation can further increase the speed of the algorithm. Our framework also allows us to incrementally update the solution of the planning problem to contend with changing conditions. We benchmark our algorithm against several recent trajectory optimization algorithms on planning problems in multiple environments. Our evaluation reveals that our approach is several times faster than previous algorithms while retaining robustness. Finally, we demonstrate the incremental version of our algorithm on replanning problems, and show that it often can find successful solutions in a fraction of the time required to replan from scratch. 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. Existing high-dimensional motion planning algorithms are simultaneously overpowered and underpowered. In domains sparsely populated by obstacles, the heuristics used by sampling-based planners to navigate “narrow passages” can be needlessly complex; furthermore, additional post-processing is required to remove the jerky or extraneous motions from the paths that such planners generate. In this paper, we present CHOMP, a novel method for continuous path refinement that uses covariant gradient techniques to improve the quality of sampled trajectories. Our optimization technique both optimizes higher-order dynamics and is able to converge over a wider range of input paths relative to previous path optimization strategies. In particular, we relax the collision-free feasibility prerequisite on input paths required by those strategies. As a result, CHOMP can be used as a standalone motion planner in many real-world planning queries. We demonstrate the effectiveness of our proposed method in manipulation planning for a 6-DOF robotic arm as well as in trajectory generation for a walking quadruped robot. 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. In this work, we present an MAV system that is able to relocalize itself, create consistent maps and plan paths in full 3D in previously unknown environments. This is solely based on vision and IMU measurements with all components running onboard and in real-time. We use visual-inertial odometry to keep the MAV airborne safely locally, as well as for exploration of the environment based on high-level input by an operator. A globally consistent map is constructed in the background, which is then used to correct for drift of the visual odometry algorithm. This map serves as an input to our proposed global planner, which finds dynamic 3D paths to any previously visited place in the map, without the use of teach and repeat algorithms. In contrast to previous work, all components are executed onboard and in real-time without any prior knowledge of the environment. In this paper, we present a real-time approach to local trajectory replanning for microaerial vehicles (MAVs). Current trajectory generation methods for multicopters achieve high success rates in cluttered environments, but assume that the environment is static and require prior knowledge of the map. In the presented study, we use the results of such planners and extend them with a local replanning algorithm that can handle unmodeled (possibly dynamic) obstacles while keeping the MAV close to the global trajectory. To ensure that the proposed approach is real-time capable, we maintain information about the environment around the MAV in an occupancy grid stored in a three-dimensional circular buffer, which moves together with a drone, and represent the trajectories by using uniform B-splines. This representation ensures that the trajectory is sufficiently smooth and simultaneously allows for efficient optimization.