How ‘inverse’ dynamics makes users smart

Arthur J. Grunwald
Faculty of Aerospace Engineering
Technion, Israel Institute of Technology
Haifa, 32000, Israel

An orbiting spacecraft creates an environment in which the laws of physics as 
experienced on the surface of the earth, do not seem to apply. Objects that are 
pushed in one direction, end up moving in the opposite direction. Likewise 
proper timing of the maneuver can have a dramatic effect on the required amount 
of maneuvering fuel. The relative motion between two co-orbiting spacecraft in 
close vicinity is counter-intuitive and difficult to understand. Therefore, it 
is almost impossible to perform proximity operations between two spacecraft on 
the basis of visual cues only, as perceived through the window of the spacecraft.

Astronauts are submitted to extensive training programs to learn to cope with 
motions in space. Therefore, maneuvering is usually restricted to the playback 
of pre-computed maneuvers, which are extensively rehearsed throughout the 
training program. Orbital maneuvering can be seen as a tightly coupled complex 
spatial optimization problem, subject to stringent operational constraints.

The ‘inverse’ method, presented in this paper provides the astronaut with 
the insight and understanding to perform fuel-efficient on-site planning and 
executing of proximity operations. In contrast to the ‘forward’ method, 
in which the astronaut has control over the maneuvering impulses, with the 
‘inverse’ method the astronaut defines the terminal conditions of the 
trajectory and its intermediate waypoints. The maneuvering impulses are computed 
in real time to match the desired trajectory. By solving the boundary conditions 
between trajectory sections, the ‘inverse’ method allows to break down the 
complex optimization problem in a series of straightforward and isolated design 
steps. A ‘waypoint stack’ is used to manage the creation and deletion of 
intermediate waypoints. The visualization of the trajectories as well as the 
operational constraints and the optimization functions, provides the astronaut 
with immediate feedback on his/her design actions. This feedback provided by 
virtue of the inverse computations, allows the astronaut to plan and execute 
complex fuel-efficient proximity operations between spacecraft, meeting 
stringent safety constraints.