We show how some geometric elements of the path of a particle moving in a plane – the osculating circle and its radius of curvature – can be used to construct the parabolic trajectory of projectiles in motion under gravity.

The trajectory planning of an aerial robotic manipulator system is studied using Hybrid Particle Swarm Optimization (HPSO). composed unmanned vehicle (UAV) base and a manipulator. dynamically singular. In addition, strong coupling exists between the UAV To overcome problems, in join space HPSO. HPSO combines superiorities PSO GA (Genetic Algorithm), prohibiting particles from becoming trapped l...

We study time averages of single particle trajectories in scale-free anomalous diffusion processes, in which the measurement starts at some time t(a)>0 after initiation of the process at t=0. Using aging renewal theory, we show that for such nonstationary processes a large class of observables are affected by a unique aging function, which is independent of boundary conditions or the external f...

In this paper, we describe trajectory planning and state estimation algorithms for aggressive flight of micro aerial vehicles in known, obstacledense environments. Finding aggressive but dynamically feasible and collision-free trajectories in cluttered environments requires trajectory optimization and state estimation in the full state space of the vehicle, which is usually computationally infe...