In this work we present a real-time approach for local trajectory replanning for MAVs. Current trajectory generation methods for multicopters achieve high success rates in cluttered environments, but assume the environment is static and require prior knowledge of the map. In our work we utilize the results of such planners and extend them with local replanning algorithm that can handle unmodeled (possibly dynamic) obstacles while keeping MAV close to the global trajectory. To make our approach real-time capable we maintain information about the environment around MAV in an occupancy grid stored in 3D circular buffer that moves together with a drone, and represent the trajectories using uniform B-splines. This representation ensures that trajectory is sufficiently smooth and at the same time allows efficient optimization.
Optimization-based approaches rely on minimizing a cost function that consists of smoothness and collision terms. The trajectory itself can be represented as a set of discrete points @cite_20 or polynomial segments @cite_11 . The approach presented in the present work falls into this category, but represents a trajectory using uniform B-splines.
@cite_20 @cite_11
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We present a novel trajectory computation algorithm to smooth piecewise linear collision-free trajectories computed by sample-based motion planners. Our approach uses cubic B-splines to generate trajectories that are C2 almost everywhere, except on a few isolated points. The algorithm performs local spline refinement to compute smooth, collision-free trajectories and it works well even in environments with narrow passages. We also present a fast and reliable algorithm for collision checking between a robot and the environment along the B-spline trajectories. We highlight the performance of our algorithm on complex benchmarks, including path computation for rigid and articulated models in cluttered environments. This paper examines techniques for finding falsifying trajectories of hybrid systems using an approach that we call trajectory splicing. Many formal verification techniques for hybrid systems, including flowpipe construction, can identify plausible abstract counterexamples for property violations. However, there is often a gap between the reported abstract counterexamples and the concrete system trajectories. Our approach starts with a candidate sequence of disconnected trajectory segments, each segment lying inside a discrete mode. However, such disconnected segments do not form concrete violations due to the gaps that exist between the ending state of one segment and the starting state of the subsequent segment. Therefore, trajectory splicing uses local optimization to minimize the gap between these segments, effectively splicing them together to form a concrete trajectory. We demonstrate the use of our approach for falsifying safety properties of hybrid systems using standard optimization techniques. As such, our approach is not restricted to linear systems. We compare our approach with other falsification approaches including uniform random sampling and a robustness guided falsification approach used in the tool S-Taliro. Our preliminary evaluation clearly shows the potential of our approach to search for candidate trajectory segments and use them to find concrete property violations. We present a new approach to motion planning using a stochastic trajectory optimization framework. The approach relies on generating noisy trajectories to explore the space around an initial (possibly infeasible) trajectory, which are then combined to produced an updated trajectory with lower cost. A cost function based on a combination of obstacle and smoothness cost is optimized in each iteration. No gradient information is required for the particular optimization algorithm that we use and so general costs for which derivatives may not be available (e.g. costs corresponding to constraints and motor torques) can be included in the cost function. We demonstrate the approach both in simulation and on a mobile manipulation system for unconstrained and constrained tasks. We experimentally show that the stochastic nature of STOMP allows it to overcome local minima that gradient-based methods like CHOMP can get stuck in. Abstract. When optimizing the performance of constrained robotic system, the motion trajectory plays a crucial role. In this research the motion planning problem for systems that admit a polynomial description of the system dynamics through differential flatness is tackled by parameterizing the system's so-called flat output as a polynomial spline. Using basic properties of B-splines, sufficient conditions on the spline coefficients are derived ensuring satisfaction of the operating constraints over the entire time horizon. Furthermore, an intuitive relaxation is proposed to tackle conservatism and a supporting software package is released. Finally, to illustrate the overall approach and potential, a numerical benchmark of a flexible link manipulator is discussed.