Animesh Chakravarthy

Obstacle avoidance in a dynamic environment: a collision cone approach

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 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.

Time-varying dynamics of a micro air vehicle with variable-sweep morphing

In this paper, we investigate the dynamics of a rapidly morphing, variable wing sweep micro air vehicle. The time scales over which the morphing occurs are of the same order as those of the flight dynamics of the MAV. We investigate the time-varying poles and zeros of this MAV for different morphing trajectories. There are several existing notions of timevarying poles and zeros of a linear time-varying system, each with its relative advantages and disadvantages. We explore the use of two of these notions in the study of the timevarying dynamics of the MAV in both the longitudinal as well as the lateral-directional axes.

Dynamics and Performance of Tailless Micro Aerial Vehicle with Flexible Articulated Wings

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.Anonlinear aero-elastic model is derived, and it is used to study the steady-state 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.

Generalization of the collision cone approach for motion safety in 3-D environments

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.

Preventing Automotive Pileup Crashes in Mixed-Communication Environments

Recent news illustrates the frequent occurrence of pileup crashes on highways. A predominant reason for the occurrence of such crashes is that current vehicles (including those equipped with an automatic cruise control system) do not provide drivers with advance information of events occurring far ahead of them. The use of intervehicular communication to provide advance warnings to enhance automotive safety is therefore being actively discussed in the research community. In this paper, we investigate scenarios wherein only a subset of the vehicles in a multivehicle stream is equipped with such advance-warning capabilities. These vehicles (which are equipped with the capability to receive far-ahead information) are arbitrarily distributed among other unequipped vehicles that are capable of receiving only local near-neighbor information. It is seen that there are conditions wherein even a partial equipage of the system can be beneficial to both equipped and unequipped vehicles in a mixed-vehicle stream. We demonstrate this through both simulations and a theoretical analysis. We also developed a prototype of an advance-warning system and conducted road tests to test the concept. These road tests have demonstrated the systems performance to be satisfactory, subject to good communication links, for the class of scenarios tested.

Collision Cones for Quadric Surfaces

The problem of collision prediction in dynamic environments appears in several diverse fields, which include robotics, air vehicles, underwater vehicles, and computer animation. In this paper, collision prediction of objects that move in 3-D environments is considered. Most work on collision prediction assumes objects to be modeled as spheres. However, there are many instances of object shapes where an ellipsoidal or a hyperboloid-like bounding box would be more appropriate. In this paper, a collision cone approach is used to determine collision between objects whose shapes can be modeled by general quadric surfaces. Exact collision conditions for such quadric surfaces are obtained in the form of analytical expressions in the relative velocity space. For objects of arbitrary shapes, exact representations of planar sections of the 3-D collision cone are obtained.

Capturability of realistic generalized true proportional navigation

The capturability of a realistic generalized true proportional navigation (RGTPN) guidance law, against a nonmaneuvering target, is analyzed. The RGTPN law is obtained by relaxing the somewhat unrealistic assumption of constant closing velocity, made in all earlier studies on generalized true proportional navigation (GTPN), and incorporating the actual time-varying value in the guidance law. Closed-form solutions for the complete capture region of RGTPN is obtained in terms of both zero and acceptable non-zero miss distances. It is shown that the capture region of RGTPN in the initial relative velocity space is significantly smaller than that of GTPN, for reasonable values of navigation constant (N) and angular direction (/spl eta/) of the missile commanded latax. However, for certain values of N and /spl eta/, capturability of RGTPN is found to be better. It is also shown that if in one of the versions of GTPN, which uses constant values of both the closing velocity and the line-of-sight (LOS) angular velocity in the guidance law the corresponding realistic time-varying quantities are used, the capture region actually expands to cover the whole of the initial relative velocity space. A number of examples are given to compare the capture performance of RGTPN with other versions of the GTPN guidance laws.

Experimental Kinematics and Dynamics of Butterflies in Natural Flight

In this paper, we discuss the collection, post-processing and subsequent evaluation of flight data of butterflies, in various free flight scenarios. The flight data is obtained by means of a vision tracking system; from which estimates of the motion of different body parts, including the head, abdomen and wings are then determined. These estimates are subsequently post-processed with a view to examining the mathematical correlations that exist between motion of individual body parts of the butterfly with its overall flight trajectory. Preliminary results performing a comparison of different takeoff sequences, are then presented.

Control Law Design for Perching an Agile MAV with Articulated Wings

This paper explores the use of variable wing dihedral and variable wing twist (in conjunction with a conventional horizontal elevator) to control an aircraft performing a perching maneuver. A choice of controller architecture wherein the dihedral is employed in the forward path and the elevator and twist are employed in the feedback path, is considered. The aircraft is modeled as a multivariable linear time-varying system. A specific perching trajectory is considered; and the open-loop aircraft is longitudinally unstable for a segment of this perching trajectory and lateral-directionally unstable for the entire perching trajectory. A multivariable time-varying controller is designed to efficiently stabilize the aircraft as well as reject longitudinal-lateral-directional wind disturbances, while closely tracking the reference perching trajectory.

Design of Notch Filters for Structural Responses with Multiaxis Coupling

A novel method for designing notch e lters to attenuate structural responses that show signie cant cross-coupling (betweenaxes )ispresented.Thisapproachdiffersfromtheconventionalmethodsinthatitisasingle-stepprocedure that enables notch e lters of each sensor path to be designed independently of those in other sensor paths while guaranteeing the stability margin requirements. As a result, this approach can result in a less conservative design as compared to the conventional methods. Thispaperdescribes theprocedure in thecontext of thecoupled lateraldirectional axes of an aircraft— the objectivebeing to gain stabilizethe structural response uniformly so as to meet the MIL-F-9490D specie cations. An example is given to illustrate the power of this method.