Craig A. Woolsey

Minimum-Time Path Planning for Unmanned Aerial Vehicles in Steady Uniform Winds

This paper is concerned with time-optimal path planning for a constant-speed unmanned aerial vehicle flying at constant altitude in steady uniform winds. The unmanned aerial vehicle is modeled as a particle moving at a constant air-relative speed and with symmetric bounds on turn rate. It is known from the necessary conditions for optimality that extremal paths comprise only straight segments and maximum-rate turns. An essential observation is that maximum-rate turns correspond to trochoidal path segments, as observed from an Earth-fixed inertial frame. The path-planning problem therefore reduces to identifying the switching points at which straight and trochoidal path segments join to form a feasible path and choosing the true minimum-time solution from the resulting set of candidate extremals. The papers primary contribution is a simple analytical solution for a subset of candidate extremal paths: those for which an initial maximum-rate turn is followed by a straight segment and then a second maximum-rate turn in the same direction as the first. The solution is easy to compute and is suitable for real-time implementation onboard an unmanned aerial vehicle with limited computational power. The remaining candidate extremal paths may be found using a simple numerical root-finding routine. The paper also shows that, for some candidate extremal paths, no corresponding Dubins path exists in the (moving) air-relative frame.

Controlled Lagrangian systems with gyroscopic forcing and dissipation

This paper describes a procedure for incorporating artificial gyroscopic forces and physical dissipation in the method of controlled Lagrangians. Energy-conserving gyroscopic forces provide additional freedom to expand the basin of stability and tune closed-loop system performance. We also study the effect of physical dissipation on the closed-loop dynamics and discuss conditions for stability in the presence of natural damping. We apply the technique to the inverted pendulum on a cart,a case study from previous papers. We develop a controller that asymptotically stabilizes the inverted equilibrium at a specific cart position for the conservative dynamic model. The region of attraction contains all states for which the pendulum is elevated above the horizontal plane. We also develop conditions for asymptotic stability in the presence of linear damping.

Moving mass control for underwater vehicles

We present two reduced-dimensional, noncanonical Hamiltonian models for a neutrally buoyant underwater vehicle coupled to an internal moving mass. It is expected that these models will be useful in designing nonlinear control laws for underwater gliders as well as for spacecraft, atmospheric re-entry vehicles, and other vehicles which use internal moving mass actuators. To illustrate, we investigate stability of a steady underwater vehicle motion using potential shaping feedback with a moving mass actuator.

Approximate Analytical Turning Conditions for Underwater Gliders: Implications for Motion Control and Path Planning

This paper describes analysis of steady motions for underwater gliders, a type of highly efficient underwater vehicle which uses gravity for propulsion. Underwater gliders are winged underwater vehicles which locomote by modulating their buoyancy and their attitude. Several underwater gliders have been developed and have proven their worth as efficient long-distance, long-duration ocean sampling platforms. Underwater gliders are so efficient because they spend much of their flight time in stable, steady motion. Wings-level gliding flight for underwater gliders has been well studied, but analysis of steady turning flight is more subtle. This paper presents an approximate analytical expression for steady turning motion for a realistic underwater glider model. The problem is formulated in terms of regular perturbation theory, with the vehicle turn rate as the perturbation parameter. The resulting solution exhibits a special structure that suggests an efficient approach to motion control as well as a planning strategy for energy efficient paths.

Underwater glider motion control

This paper describes an underwater glider motion control system intended to enhance locomotive efficiency by reducing the energy expended by vehicle guidance. In previous work, the authors derived an approximate analytical expression for steady turning motion by applying regular perturbation theory to a realistic vehicle model. The analysis results suggested the use of a well-known time-optimal path planning procedure developed for the Dubins car, an often-used model of a wheeled mobile robot. For underwater gliders operating at their most efficient flight condition, time-optimal glide paths correspond to energy-optimal glide paths. Thus, an analytically informed strategy for energy-efficient locomotion is to generate sequences of steady wings-level and turning motions according to the Dubins path planning procedure. Because the turning motion results are only approximate, however, and to compensate for model and environmental uncertainty, one must incorporate feedback to ensure convergent path following. This paper describes the dynamic modelling of the complete multi-body control system and the development and numerical implementation of a motion control system. The control system can be combined with a higher level guidance strategy involving Dubins-like paths to achieve energy-efficient locomotion.

Stabilizing underwater vehicle motion using internal rotors

As a case study of a particular control methodology and as a practical contribution in the area of underwater vehicle control, we consider the problem of stabilizing an underwater vehicle using internal rotors as actuators. The control design method comprises three steps. The first step involves shaping the kinetic energy of the conservative dynamics. For the underwater vehicle, the control term from this step may be interpreted as modifying the system inertia. In the second step, we design feedback dissipation using a Lyapunov function constructed in the first step. In the third step, we include a general model for the viscous force and moment on the vehicle and we show that these effects enhance stability. We first apply this method to a vehicle whose centers of buoyancy and gravity coincide and then to a vehicle with noncoincident centers of buoyancy and gravity.

Modeling, Identification, and Control of an Unmanned Surface Vehicle

This paper describes planar motion modeling for an unmanned surface vehicle (USV), including a comparative evaluation of several experimentally identified models over a wide range of speeds and planing conditions. The modeling and identification objective is to determine a model that is sufficiently rich to enable effective model-based control design and trajectory optimization, sufficiently simple to allow parameter identification, and sufficiently general to describe a variety of hullforms and actuator configurations. We focus, however, on a specific platform: a modified rigid hull inflatable boat with automated throttle and steering. Analysis of experimental results for this vessel indicates that Nomotos first-order steering model provides the best compromise between simplicity and fidelity at higher speeds. At low speeds, it is helpful to include a first-order lag model for sideslip. Accordingly, we adopt a multiple model approach in which the model structure and parameter values are scheduled based on the nominal forward speed. The speed-scheduled planar motion model may be used to generate dynamically feasible trajectories and to develop trajectory tracking control laws. The paper describes the development, analysis, and experimental implementation of two trajectory tracking control algorithms: a cascade of proportional-derivative controllers and a nonlinear controller obtained through backstepping. Experimental results indicate that the backstepping controller is much more effective at tracking trajectories with highly variable speed and course angle.

Reduced Hamiltonian Dynamics for a Rigid Body/Mass Particle System

Three equivalent reduced-dimensional Hamiltonian systems that model a rigid body in a perfect fluid coupled to am oving-mass particle are presented. These Hamiltonian systems describe the dynamics of an underwater vehicle with a moving-mass actuator or a flexible internal appendage. The systems include, as a special case, models for a spacecraft coupled to a moving mass. The Hamiltonian models are noncanonical; the structure of Hamilton’s equations is defined by the Poisson tensor, a generalization of the symplectic matrix from classical mechanics. The three models presented trade complexity of the generalized inertia tensor for complexity of the Poisson tensor. One model has a highly coupled inertia tensor and a block-diagonal Poisson tensor, whereas another has a highly coupled Poisson tensor and a block-diagonal inertia tensor. Two cases are considered. The first is that of an unconstrained mass particle. The second is that of a mass particle constrained to move in a linear track. Examples are included to illustrate the use of these models for nonlinear stability analysis.

The need for higher-order averaging in the stability analysis of hovering, flapping-wing flight

Because of the relatively high flapping frequency associated with hovering insects and flapping wing micro-air vehicles (FWMAVs), dynamic stability analysis typically involves direct averaging of the time-periodic dynamics over a flapping cycle. However, direct application of the averaging theorem may lead to false conclusions about the dynamics and stability of hovering insects and FWMAVs. Higher-order averaging techniques may be needed to understand the dynamics of flapping wing flight and to analyze its stability. We use second-order averaging to analyze the hovering dynamics of five insects in response to high-amplitude, high-frequency, periodic wing motion. We discuss the applicability of direct averaging versus second-order averaging for these insects.

Path planning for efficient UAV coordination in aerobiological sampling missions

This paper is concerned with the coordinated flight of two autonomous UAVs to be used for aerobiological sampling of biological threat agents above agricultural fields. The periodic sampling task involves two phases: a sampling interval and an initialization interval. During the sampling interval, both vehicles must employ their aerobiological sampling devices and follow a precise ground track in the presence of sustained winds. During the initialization interval, the vehicles move to their respective initial states to begin the next sampling interval. To maximize the volume of air sampled by the UAVs during an individual sampling mission, the initialization interval must be as short as possible. The paper provides a simple, geometric method for generating candidate time optimal paths in steady winds, based on Dubins¿ well-known results for minimum time paths of bounded curvature. The approach is used to generate paths for both UAVs, which must coordinate their motion along their respective paths in order to avoid collision. The described methods were tested during an aerobiological sampling experiment focusing on the plant pathogen Phytophthora infestans.