Sasi Prabhakaran Viswanathan

Guidance and Control for Spacecraft Autonomous Chasing and Close Proximity Maneuvers

Abstract Autonomous rendezvous and proximity operations between a chaser (or pursuer) spacecraft and a target space object consist of autonomous controlled approach and controlled docking with or controlled capture of the target by the chaser. Guidance, navigation and control problems during autonomous rendezvous and proximity maneuvers between spacecraft are challenging, particularly when the target spacecraft or space object is not cooperating with the chaser spacecraft. In this work, we present a guidance scheme and a control scheme for a chaser spacecraft that is tasked to synchronize its motion with a target space object during close proximity maneuvers. The guidance scheme generates a desired state trajectory based on remote measurements of the motion states of the target from the chaser and motion prediction of the target. The tracking control scheme for the chaser results in asymptotic tracking of the desired state trajectory with an almost global domain of convergence on the state space. These schemes are applied to the situation where the chaser spacecraft synchronizes its attitude motion with the target, while maintaining a constant relative position with respect to the target at the end of the maneuver. Numerical simulation results are presented to show the performance of these guidance and tracking control schemes.

Dynamics and Control of Spacecraft With a Generalized Model of Variable Speed Control Moment Gyroscopes

The attitude dynamics model for a spacecraft with a variable speed control moment gyroscope (VSCMG) is derived using the principles of variational mechanics. The resulting dynamics model is obtained in the framework of geometric mechanics, relaxing some of the assumptions made in prior literature on control moment gyroscopes (CMGs). These assumptions include symmetry of the rotor and gimbal structure, and no offset between the centers of mass of the gimbal and the rotor. The dynamics equations show the complex nonlinear coupling between the internal degrees-of-freedom associated with the VSCMG and the spacecraft base bodys rotational degrees-of-freedom. This dynamics model is then further generalized to include the effects of multiple VSCMGs placed in the spacecraft base body, and sufficient conditions for nonsingular VSCMG configurations are obtained. General ideas on control of the angular momentum of the spacecraft using changes in the momentum variables of a finite number of VSCMGs are provided. A control scheme using a finite number of VSCMGs for attitude stabilization maneuvers in the absence of external torques and when the total angular momentum of the spacecraft is zero is presented. The dynamics model of the spacecraft with a finite number of VSCMGs is then simplified under the assumptions that there is no offset between the centers of mass of the rotor and gimbal, and the rotor is axisymmetric. As an example, the case of three VSCMGs with axisymmetric rotors, placed in a tetrahedron configuration inside the spacecraft, is considered. The control scheme is then numerically implemented using a geometric variational integrator (GVI). Numerical simulation results with zero and nonzero rotor offset between centers of mass of gimbal and rotor are presented.

Decentralized guidance and control for spacecraft formation flying using virtual leader configuration

This paper proposes a novel guidance and control scheme for decentralized spacecraft formation flying on SE(3) via virtual leader configuration. The configuration space for a spacecraft modeled as a rigid body is the Lie group SE(3), which is the set of positions and orientations of the spacecraft moving in three-dimensional Euclidean space. A combined guidance and feedback control law in continuous time for the full (translational and rotational) motion of a rigid body under the influence of external disturbance is designed. The guidance scheme aims to reach a final relative configuration according to the desired formation where the relative configuration is described in terms of the exponential coordinates on SE(3). The control law then obtains the desired trajectory leading to the desired formation. The stability of the feedback control system is analyzed. Numerical simulation results demonstrates that the control law can effectively perform a decentralized formation flying for a selected rigid spacecraft formation between three spacecraft.

Robust stabilization of rigid body attitude motion in the presence of a stochastic input torque

This paper investigates robust asymptotic stabilization of rigid body attitude dynamics evolving on the tangent bundle of SO(3) using geometric stochastic feedback control, where the system is subject to a stochastic input torque. To start with, the attitude dynamics is interpreted in the Ito sense. However, due to evolution of the kinematic differential equation of the system on SO(3), analyzing the stochastic system on TSO(3) is non-trivial. To address this challenging problem of robust asymptotic stabilization of attitude dynamics, the back-stepping method along with a suitable Morse-Lyapunov (M-L) function candidate with constant control gain parameters are used to obtain a nonlinear stochastic feedback control law. The control gain matrix and the M-L function control gain can be obtained by solving a feasible LMI, which can guarantee the robust asymptotic stability of the rigid body on TSO(3). Numerical simulations are performed to demonstrate and validate the effectiveness of the proposed controller in the state space of rigid body attitude motion in TSO(3).

Integrated Guidance and Feedback Control of Underactuated Robotics System in SE(3)

An integrated guidance and feedback control scheme for steering an underactuated vehicle through desired waypoints in three-dimensional space, is developed here. The underactuated vehicle is modeled as a rigid body with four control inputs. These control inputs actuate the three degrees of freedom of rotational motion and one degree of freedom of translational motion in a vehicle body-fixed coordinate frame. This actuation model is appropriate for a wide range of underactuated vehicles including spacecraft with internal attitude actuators, vertical take-off and landing (VTOL) aircraft, fixed-wing multirotor unmanned aerial vehicles (UAVs), maneuverable robotic vehicles, etc. The guidance problem is developed on the special Euclidean group of rigid body motions, SE(3), in the framework ofgeometric mechanics, which represents the vehicle dynamics globally on this configuration manifold. The integrated guidance and control algorithm selects the desired trajectory for the translational motion that passes through the given waypoints, and the desired trajectory for the attitude based on the desired thrust direction to achieve the translational motion trajectory. A feedback control law is then obtained to steer the underactuated vehicle towards the desired trajectories in translation and rotation. This integrated guidance and control scheme takes into account known bounds on control inputs and generates a trajectory that is continuous and at least twice differentiable, which can be implemented with continuous and bounded control inputs. The integrated guidance and feedback control scheme is applied to an underactuated quadcopter UAV to autonomously generate a trajectory through a series of given waypoints in SE(3) and track the desired trajectory in finite time. The overall stability analysis of the feedback system is addressed. Discrete time models for the dynamics and control schemes of the UAV are obtained in the form of Lie group variational integrators using the discrete Lagrange-d’Alembert principle. Almost global asymptotic stability of the feedback system over its state space is shown analytically and verified through numerical simulations.

Design of an Adaptive Singularity-Free Control Moment Gyroscope (ASCMG) Cluster for Spacecraft Attitude Control

Spacecraft attitude control using an Adaptive Singularity-free Control Moment Gyroscope (ASCMG) cluster design for internal actuation is presented. A complete dynamics model is derived using the principles of variational mechanics, relaxing some common assumptions made in prior literature on control moment gyroscopes. These assumptions include perfect axisymmetry of the rotor and gimbal structures, and perfect alignment of the centers of mass of the gimbal and the rotor. The resulting dynamics display complex nonlinear coupling between the internal degrees of freedom associated with the CMG and the spacecraft base body’s rotational degrees of freedom in the absence of these assumptions. This dynamics model is further generalized to include the effects of multiple CMGs placed in the spacecraft bus, and sufficient conditions for non-singular CMG cluster configurations are obtained. General ideas on control of the angular momentum of the spacecraft using changes in the momentum variables of a finite number of CMGs, are provided. A control scheme using a finite number of CMGs in the absence of external torques and when the total angular momentum of the spacecraft is zero, is presented. The dynamics model of the spacecraft with a finite number of CMGs is then simplified under the assumption that the rotor is axisymmetric, in which case it is shown that singularities are avoided. As an example, the case of three CMGs with axisymmetric rotors, placed in a tetrahedron configuration inside the spacecraft, is considered. The control scheme is then numerically implemented using a geometric variational integrator and the results confirm the singularity-free property and high control authority of the ASCMG cluster. Moreover, as rotor misalignments are addressed in the dynamics model, the ASCMG cluster can adapt to them without requiring hardware changes.Copyright

The Reaction Mass Biped: Geometric Mechanics and Control

Inverted Pendulum based reduced order models offer many valuable insights into the much harder problem of bipedal locomotion. While they help in understanding leg behavior during walking, they fail to capture the natural balancing ability of humans that stems from the variable rotational inertia on the torso. In an attempt to overcome this limitation, the proposed work introduces a Reaction Mass Biped (RMB). It is a generalization of the previously introduced Reaction Mass Pendulum (RMP), which is a multi-body inverted pendulum model with an extensible leg and a variable rotational inertia torso. The dynamical model for the RMB is hybrid in nature, with the roles of stance leg and swing leg switching after each cycle. It is derived using a variational mechanics approach, and is therefore coordinate-free. The RMB model has thirteen degrees of freedom, all of which are considered to be actuated. A set of desired state trajectories that can enable bipedal walking in straight and curved paths are generated. A control scheme is then designed for asymptotically tracking this set of trajectories with an almost global domain-of-attraction. Numerical simulation results confirm the stability of this tracking control scheme for different walking paths of the RMB. Additionally, a discrete dynamical model is also provided along-with an appropriate Geometric Variational Integrator (GVI). In contrast to non-variational integrators, GVIs can better preserve energy terms for conservative mechanical systems and stability properties (achieved through energy-like lyapunov functions) for actuated systems.

Feedback tracking control schemes for a class of underactuated vehicles in SE(3)

A trajectory tracking control scheme for a class of underactuated vehicles is presented here. The underactuated vehicle is modeled as a rigid body to which control thrust is applied along a single body-fixed axis and control torque can be applied along all three body-fixed coordinate axes. The combined rotational and translational motion of the rigid body is underactuated with the degree of underactuation two. Such an actuation scheme is reflective of a wide range of vehicles such as vertical take-off and landing (VTOL) aircraft, fixed-wing aircraft, and quadcopter uncrewed aerial vehicles (UAVs). For this class of underactuated vehicles, the proposed controller gives exponential stabilization of the position tracking error. Additionally, the component of the angular velocity parallel to the thrust direction, is regulated to be zero under the proposed control scheme. The other two components of the angular velocity track desired profiles that lead to exponential stabilization of the desired position trajectory; this angular velocity tracking control scheme is finite time stable. The combination of these schemes leads to guaranteed exponential stability of the overall feedback control scheme. A set of numerical simulation results that illustrate the performance of the overall feedback tracking control scheme is provided.

Design of an Adaptive Singularity-free Control Moment Gyroscope (ASCMG) actuator for agile and precise attitude control of cubesat

Design considerations for agile, precise and reliable attitude control of micro-spacecraft using Adaptive Singularity-free Control Moment Gyroscope (ASCMG) actuators are presented here. A complete dynamics model of a spacecraft with an ASCMG is derived using the principles of variational mechanics, relaxing some assumptions made in prior literature on Control Moment Gyroscopes (CMG). The dynamics so obtained shows the complex nonlinear coupling between the internal degrees of freedom associated with an ASCMG and the spacecraft base bodys attitude motion. By default, the general ASCMG model is equivalent to that of a Variable Speed Control Moment Gyroscope without symmetrical rotor and gimbal, and can operate as a CMG by spinning the rotor at constant speed. This dynamics model is then extended to include the effects of multiple ASCMGs placed in the spacecraft bus, and sufficient conditions for non-singular ASCMG cluster configurations are obtained to operate the cluster in CMG mode. The adverse effects of the simplifying assumptions that lead to the standard CMG design, and how they lead to CMG singularities, are described. A bare minimum hardware prototype of an ASCMG using low cost COTS components, is shown. A control scheme for agile and precise attitude pointing control of a cubesat using a finite number of ASCMGs in the absence of external torques, is presented. A Geometric Variational Integration scheme is obtained for this multibody spacecraft for numerical and micro-controller implementation.