ABSTRACT
In this chapter, we consider the control distribution problem for highly overactuated systems. In the case of over-actuated systems, there is redundancy in the total number of actuators, compared to the number of equations of motion that govern the dynamics of the system. For example, in the F-16 aircraft, two-axis thrust vectoring is used along with conventional control surfaces (ailerons, rudder, and elevator) and the throttle, resulting in seven control inputs to produce six net control forces and moment components needed to control the six degrees of freedom. As a second example, consider the attitude control of a satellite. Frequently there will be two sets of actuators: one set consists of twelve on-off small jets or thrusters configured in six pairs such that one pair can cause a positive pitch rotation, and another pair can cause a negative pitch rotation, and so on for the other three axes of rotation. The firing direction of the thrusters can be changed so that each pair can also cause pure translations in each of the three directions. This is precisely the pattern used for translational and pointing control for the space shuttle. These on-off thrusters result in bang-bang control and are not suitable for fine pointing. For many spacecraft, a second set of actuators, namely momentum exchange devices (such as control moment gyros), are incorporated into the system design to allow smooth, variable-amplitude torques for precision maneuvers. A minimum of three control moment gyros are required to generate a torque in any commanded direction, but normally four or more are used to allow redundancy, increased torque capability, and to avoid certain singular conditions that arise for such momentum transfer devices [77]. The space station utilizes four control moment gyros for the primary attitude control system. The combination of the twelve thrusters and four momentum
exchange devices provides a significant level of redundancy to increase the frequency bandwidth and allow flexible budgeting of fuel and electricity as well as lead to increased reliability. Generally, control distribution approaches exploit the set of actuation possibilities using some “best actuation commands” to achieve the desired system state change, while taking into account constraints on individual actuators, power, and fuel reserves, avoiding undesirable actuation configurations or singularities, and similar considerations. The current state of the practice has been successfully targeted on specific physical systems with fewer than twenty actuators for up to six degrees of freedom. The present chapter seeks to generalize these conventional ideas so that massively redundant actuation can be accommodated for the high-dimensioned systems anticipated for the future.
