Abstract-A novel collision cone approach is proposed as an aid to collision detection and avoidance between irregularly shaped moving objects with unknown trajectories. It is shown that the collision cone can be effectively used to determine whether collision between a robot and an obstacle (both moving in a dynamic environment) is imminent. No restrictions are placed on the shapes of either the robot or the obstacle, i.e., they can both be of any arbitrary shape. The collision cone concept is developed in a phased manner starting from existing analytical results-available in aerospace literature-that enable prediction of collision between two moving point objects. These results are extended to predict collision between a point and a circular object, between a point and an irregularly shaped object, between two circular objects, and finally between two irregularly shaped objects. Using the collision cone approach, several strategies that the robot can follow in order to avoid collision, are presented. A discussion on how the shapes of the robot and obstacles can be approximated in order to reduce computational burden is also presented. A number of examples are given to illustrate both collision prediction and avoidance strategies of the robot.

The purpose of this paper is to analyze and discuss the performance and stability of a tailless micro aerial vehicle with flexible articulated wings. The dihedral angles can be varied symmetrically on both wings to control the aircraft speed independently of the angle of attack and flight-path angle, while an asymmetric dihedral setting can be used to control yaw in the absence of a vertical tail. A nonlinear aeroelastic model is derived, and it is used to study the steadystate performance and flight stability of the micro aerial vehicle. The concept of the effective dihedral is introduced, which allows for a unified treatment of rigid and flexible wing aircraft. It also identifies the amount of elasticity that is necessary to obtain tangible performance benefits over a rigid wing. The feasibility of using axial tension to stiffen the wing is discussed, and, at least in the context of a linear model, it is shown that adding axial tension is effective but undesirable. The turning performance of an micro aerial vehicle with flexible wings is compared to an otherwise identical micro aerial vehicle with rigid wings. The wing dihedral alone can be varied asymmetrically to perform rapid turns and regulate sideslip. The maximum attainable turn rate for a given elevator setting, however, does not increase unless antisymmetric wing twisting is employed.

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In this paper, the longitudinal dynamics of a fast-morphing, variable-wing-sweep micro air vehicle are investigated from a flight dynamics perspective. The time scales over which the morphing occurs are of the same order as the flight dynamics of the micro air vehicle, due to which the time-varying aspects of the dynamics must be carefully evaluated. The time-varying characteristic equation (which represents a generalization of the standard linear time-invariant characteristic equation) for this micro air vehicle is presented in analytic form, and this enables a characterization of the influence of different morphing trajectories on the flight dynamics. The concept of a timevarying pole is subsequently adopted and the flight dynamic properties of the time-varying modes are determined. A tool to properly evaluate the sensitivity of the time-varying modes to different morphing trajectories is demonstrated. Nomenclature A 0 t, A 1 t, A 2 t, A 3 t = coefficients of time-varying characteristic equation E i t = energy associated with ith mode F x = derivative of generalized force F with respect to state x g = acceleration due to gravity, m=s 2

Avoidance of collision between moving objects in a 3-D environment is fundamental to the problem of planning safe trajectories in dynamic environments. This problem appears in several diverse fields including robotics, air vehicles, underwater vehicles and computer animation. Most of the existing literature on collision prediction assumes objects to be modelled as spheres. While the conservative spherical bounding box is valid in many cases, in many other cases, where objects operate in close proximity, a less conservative approach, that allows objects to be modelled using analytic surfaces that closely mimic the shape of the object, is more desirable. In this paper, a collision cone approach (previously developed only for objects moving on a plane) is used to determine collision between objects, moving in 3-D space, whose shapes can be modelled by general quadric surfaces. Exact collision conditions for such quadric surfaces are obtained and used to derive dynamic inversion based avoidance strategies.