ATTITUDE CONTROL ON SO(3) WITH PIECEWISE SINUSOIDS

This dissertation addresses rigid body attitude control with piecewise sinusoidal signals. We consider rigid-body attitude kinematics on SO(3) with a class of sinusoidal inputs. We present a new closed-form solution of the rotation matrix kinematics. The solution is analyzed and used to prove controllability. We then present kinematic-level orientation-feedback controllers for setpoint tracking and command following. Next, we extend the sinusoidal kinematic-level control to the dynamic level. As a representative dynamic system, we consider a CubeSat with vibrating momentum actuators that are driven by small $\epsilon$-amplitude piecewise sinusoidal internal torques. The CubeSat kinetics are derived using Newton-Euler\u27s equations of motion. We assume there is no external forcing and the system conserves zero angular momentum. A second-order approximation of the CubeSat rotational motion on SO(3) is derived and used to derive a setpoint tracking controller that yields order O(ε2) closed-loop error. Numerical simulations are presented to demonstrate the performance of the controls. We also examine the effect of the external damping on the CubeSat kinetics. In addition, we investigate the feasibility of the piecewise sinusoidal control techniques using an experimental CubeSat system. We present the design of the CubeSat mechanical system, the control system hardware, and the attitude control software. Then, we present and discuss the experiment results of yaw motion control. Furthermore, we experimentally validate the analysis of the external damping effect on the CubeSat kinetics

Energetics Of Control Moment Gyroscopes In Robotic Joint Actuation

Control moment gyros (CMGs) are an energy-efficient means of reactionless actuation currently used for attitude control in some spacecraft. In this work, CMGs are compared to direct-drive actuation for robotic applications. Torque, power, and energy of the gimbal motor are calculated using principles of angular momentum and virtual power. Scissored-pair CMGs produce output torque along the joint axis, facilitating comparison with joint motors. A mechanical coupling enforcing scissored-pair symmetry eliminates undesirable gyroscopic reaction torques and accompanying power costs while simplifying analysis. Strictly controlling CMG rotor speed doubles the CMGs? energy costs, whereas implementing minimal rotor speed control while assuming constant rotor speed reduces the energy costs without compromising the analyses. A single-link robot actuated with scissored-pair CMGs uses the same energy as direct drive for a large range of gimbal inertias and maximum gimbal angles. The transverse rate of the robot base does not affect this result if angular momentum is conserved about the joint axis. The equations of motion for an n-link robot with CMGs are presented in a recursive form. A two-link robot with orthogonal joint axes and axisymmetric bodies reduces to two, independent, single-link robots. In contrast, a two-link robot with parallel joint axes favors CMGs when the joints rotate with opposite sign, e.g. reaching motions. Direct drive is preferred when the joints act in unison, e.g. throwing motions. Conceptually, CMGs and direct drive may be analyzed as idealized body and joint torques, respectively. The mappings from actuator torques and velocities to generalized torques and velocities explain differences in power cost between the two actuation methods. A proposed power-optimal robot includes both types of actuation. The optimal distribution of joint and body torques for two- and three-link planar robots is calculated and applied to a three-link robot tracing a closed triangle. The combined actuation method easily outperforms the others in a Monte Carlo simulation. A planar robot with joint motors and CMGs currently in development illustrates the design of a CMG-actuated robot