Title / Abstract / Contents / Part 1 / Part 2 / Part 3 /
Prev./ Next

TWO POSSIBLE NAVIGATION MODELS: INTRODUCTION

To better visualize the application of the navigation model in a lunar navigation system, two hypothetical systems will be described. Since dead reckoning is the basic form of navigation, these systems will be primarily lunar dead reckoning machines, supplemented by periodic fixing.

Hung [1970] derives a set of dead reckoning equations which may be considered a model of lunar navigation. The model is based on lunar spherical coordinates, and consists of a set of equations that give the location of the vehicle in lunar latitude, longitude, and radial distance, based on the vehicle's velocity vector and time. This will be considered the basis of a high-fidelity model of lunar navigation. Hung also includes a set of simplified dead reckoning equations based on a two-dimensional cartesian coordinate system, rather than the lunar sphere. The second model is an extraction of the more accurate primary model, and is suitable only for local area navigation. This will be the basis of a low-fidelity model of lunar navigation.

The models are by no means a definitive categorization of lunar surface navigation, but they were selected as a way of progressing from less complex concepts to more complex concepts. No attempt was made to select the most optimum design; they are simply for demonstration purposes.



LOW-FIDELITY DEAD RECKONING SCHEMES

The low-fidelity dead reckoning model, while simple, has many practical applications for local navigation tasks requiring only moderate accuracy. The scheme described here is very similar to that used in the Apollo Lunar Rover (LRV), a system which performed very well in actual lunar operations. The Apollo LRV is described more extensively in part 2.

In this model, the lunar environment is represented by a level, 2-dimensional plane. The surface is assumed to be smooth, with no errors introduced by excess measurement of distance over small obstacles. Measurement of vehicle heading is assumed to be equivalent to measurement of course, and wheel slippage is assumed to be zero. While longitude lines in spherical coordinates converge as they approach the lunar poles, the longitude lines in this model are assumed to be everywhere parallel. This is not true to reality, but it is a suitable representation of small areas of the Moon, especially near lunar equatorial regions. A schematic representation of the model is given in Figure 5. Scaling of coordinates is arbitrary. The Apollo LRV used a scale of kilometers.




Figure 5. The low-fidelity navigation model.

A distinction must be made between the concept of course and of heading: Course is the direction that a vehicle or vessel is traveling, heading is the direction that the vehicle is pointed in. For craft that travel in a moving fluid medium, such as aircraft or ships, velocity vector may be different than heading. While a lunar vehicle is not traveling in a fluid medium, its velocity vector may be different than heading, since slipping and skidding may occur. Measuring the vehicle's heading does not necessarily establish the vehicle's true displacement vector, but assuming they are the same should incur only small errors.

Prev./ Next