Dynamics and Control of Tethered Formation Flight Spacecraft Using the SPHERES Testbed

This paper elaborates on the theory and experiment of controlling tethered spacecraft formation without depending on thrusters. In dealing with such underactuated systems, much emphasis is placed on complete decentralization of the control and estimation algorithms in order to reduce the dimensionality and complication. The nonlinear equations of motions of multi-vehicle tethered spacecraft are derived by Lagrange’s equations. Decentralization is then realized by the diagonalization technique and its stability is proven by contraction theory. The preliminary analysis predicts unstable dynamics depending on the direction of the tether motor. The controllability analysis indicates that both array resizing and spin-up are fully controllable only by the reaction wheels and the tether motor, thereby eliminating the need for thrusters. Based upon this analysis, gain-scheduling LQR controllers and nonlinear controllers by feedback linearization have been successfully implemented into the tethered SPHERES testbed, and tested at the NASA MSFCs flat floor facility using two and three SPHERES configurations. The relative sensing mechanism employing the ultrasound ranging system and the inertial gyro is also described

Nonlinear control and synchronization of multiple Lagrangian systems with application to tethered formation flight spacecraft

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 217-228).This dissertation focuses on the synchronization of multiple dynamical systems using contraction theory, with applications to cooperative control of multi-agent systems and synchronization of interconnected dynamics such as tethered formation flight. Inspired by stable combinations of biological systems, contraction nonlinear stability theory provides a systematic method to reduce arbitrarily complex systems into simpler elements. One application of oscillation synchronization is a fully decentralized nonlinear control law, which eliminates the need for any inter-satellite communications. We use contraction theory to prove that a nonlinear control law stabilizing a single-tethered spacecraft can also stabilize arbitrarily large circular arrays of tethered spacecraft, as well as a three-spacecraft inline configuration. The convergence result is global and exponential due to the nature of contraction analysis. The proposed decentralized control strategy is further extended to robust adaptive control in order to account for model uncertainties. Numerical simulations and experimental results validate the exponential stability of the tethered formation arrays by implementing a tracking control law derived from the reduced dynamics.(cont.) This thesis also presents a new synchronization framework that can be directly applied to cooperative control of autonomous aerospace vehicles and oscillation synchronization in robotic manipulation and locomotion. We construct a dynamical network of multiple Lagrangian systems by adding diffusive couplings to otherwise freely moving or flying vehicles. The proposed tracking control law synchronizes an arbitrary number of robots into a common trajectory with global exponential convergence. The proposed control law is much simpler than earlier work in terms of both the computational load and the required signals. Furthermore, in contrast with earlier work which used simple double integrator models, the proposed method permits highly nonlinear systems and is further extended to adaptive synchronization, partial-joint coupling, and concurrent synchronization. Another contribution of the dissertation is a novel nonlinear control approach for underactuated tethered formation flight spacecraft. This is motivated by a controllability analysis that indicates that both array resizing and spin-up are fully controllable by the reaction wheels and the tether motor. This work reports the first propellant-free underactuated control results for tethered formation flight.(cont.) We also fulfill the potential of the proposed strategy by providing a new momentum dumping method. This dissertation work has evolved based on the research philosophy of balancing theoretical work with practicality, aiming at physically intuitive algorithms that can be directly implemented in real systems. In order to validate the effectiveness of the decentralized control and estimation framework, a new suite of hardware has been designed and added to the SPHERES (Synchronize Position Hold Engage and Reorient Experimental Satellite) testbed. Such recent improvements described in this dissertation include a new tether reel mechanism, a force-torque sensor and an air-bearing carriage with a reaction wheel. This thesis also introduces a novel relative attitude estimator, in which a series of Kalman filters incorporate the gyro, force-torque sensor and ultrasound ranging measurements. The closed-loop control experiments can be viewed at ...by Soon-Jo Chung.Sc.D

Propellant-Free Control of Tethered Formation Flight, Part 2: Nonlinear Underactuated Control

This is the second in a series of papers that exploit the physical coupling of tethered spacecraft to derive a propellant-free spin-up and attitude control strategy. We take a nonlinear control approach to underactuated tethered formation flying spacecraft, whose lack of full state feedback linearizability, along with their complex nonholonomic behavior, characterizes the difficult nonlinear control problem. We introduce several nonlinear control laws that are more efficient in tracking time-varying trajectories than linear control. We also extend our decentralized control approach to underactuated tethered systems, thereby eliminating the need for any intersatellite communication. To our knowledge, this work reports the first nonlinear control results for underactuated tethered formation flying spacecraft. This article further illustrates the potential of the proposed strategy by providing a new momentum dumping method that does not use torque-generating thrusters

Nonlinear Model Reduction and Decentralized Control of Tethered Formation Flight by Oscillation Synchronization

This paper describes a fully decentralized nonlinear control law for spinning tethered formation flight, based on exploiting geometric symmetries to reduce the original nonlinear dynamics into simpler stable dynamics. Motivated by oscillation synchronization in biological systems, we use contraction theory to prove that a control law stabilizing a single-tethered spacecraft can also stabilize arbitrary large circular arrays of spacecraft, as well as the three inline configuration. The convergence result is global and exponential. Numerical simulations and experimental results using the SPHERES testbed validate the exponential stability of the tethered formation arrays by implementing a tracking control law derived from the reduced dynamics

Dynamics and Control of Tethered Formation Flight Spacecraft Using the SPHERES Testbed

This paper elaborates on the theory and experiment of controlling tethered spacecraft formation without depending on thrusters. In dealing with such underactuated systems, much emphasis is placed on complete decentralization of the control and estimation algorithms in order to reduce the dimensionality and complication. The nonlinear equations of motions of multi-vehicle tethered spacecraft are derived by Lagrange’s equations. Decentralization is then realized by the diagonalization technique and its stability is proven by contraction theory. The preliminary analysis predicts unstable dynamics depending on the direction of the tether motor. The controllability analysis indicates that both array resizing and spin-up are fully controllable only by the reaction wheels and the tether motor, thereby eliminating the need for thrusters. Based upon this analysis, gain-scheduling LQR controllers and nonlinear controllers by feedback linearization have been successfully implemented into the tethered SPHERES testbed, and tested at the NASA MSFCs flat floor facility using two and three SPHERES configurations. The relative sensing mechanism employing the ultrasound ranging system and the inertial gyro is also described

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

Motion Coordination of Aerial Vehicles

The coordinated motion control of multiple vehicles has emerged as a field of major interest in the control community. This thesis addresses two topics related to the control of a group of aerial vehicles: the output feedback attitude synchronization of rigid bodies and the formation control of Unmanned Aerial Vehicles (UAVs) capable of Vertical Take-Off and Landing (VTOL). The information flow between members of the team is assumed fixed and undirected. The first part of this thesis is devoted to the attitude synchronization of a group of spacecraft. In this context, we propose control schemes for the synchronization of a group of spacecraft to a predefined attitude trajectory without angular velocity measurements. We also propose some velocity-free consensus-seeking schemes allowing a group of spacecraft to align their attitudes, without reference trajectory specification. The second part of this thesis is devoted to the control of a group of VTOL-UAVs in the Special Euclidian group SE(3), i.e., position and orientation. In this context, we propose a few position coordination schemes without linear-velocity measurements. We also propose some solutions to the same problem in the presence of communication time-delays between aircraft. To solve the above mentioned problems, several new technical tools have been introduced in this thesis to overcome the deficiencies of the existing techniques in this field