Shinji Hokamoto

FormulaTion and Control of Space-based Flexible Robots with Slewing-deployable Links

Abstract The present study deals with a space-based variable geometry mobile manipulator with an arbitrary number of modules, each with two flexible links: one of them free to slew (revolute joint); and the other deployable (prismatic joint). The versatile manipulator has several attractive features: favorable obstacle avoidance, absence of singular configurations, reduced inertia coupling, relatively simpler inverse kinematics as well as governing equations of motion, to mention a few. To begin with, derivation of the governing equations of motion, using the Lagrangian procedure, is explained. As can be expected, the recursive equations are highly nonlinear, nonautonomous and coupled. This is followed by the development of a numerical algorithm leading to the solution for the inverse kinematics. Finally, some typical simulation results for trajectory control of the end-effector using the resolved acceleration approach are presented. They clearly emphasize importance of the control strategy based on the flexible manipulator model.

Position and attitude control of an underactuated satellite with constant thrust

This paper discusses a position and attitude control problem of an underactuated satellite which uses on-off thruster mechanisms for control. Each thrusters has constant orientation relative to the satellite’s body, and can generate only unilateral forces. The purpose of this paper is to clarify the control law for simultaneous position and attitude control for this type of satellite configuration. Considering the input constraints, we obtain the analytical solutions of the satellite’s translational and rotational motion. Then the control procedure utilizing an invariant manifold is derived. Some numerical simulations are shown to verify the effectiveness of the proposed controller.

Position and attitude control of a planar satellite by two thrusters

This study deals with the in-plane motion of a free-floating planar satellite equipped with two thrusters whose force directions are fixed with respect to the satellite. The system’s governing equations form non-integrable second-order “nonholonomic” constraints due to the fixed force directions within the satellite. First, this paper shows the general expressions of the system’s equations of motion, and shows that its translational and rotational motions can not be controlled independently. Next, by assuming an imaginary thruster controlled by a feedback law, we transform the nonholonomic constraints into holonomic ones. This concept is followed by a strategy to achieve a rotational motion without drift for a satellite system with two fixed thrusters. Afterwards, this paper shows a procedure for precise control of the position and attitude of the system. The validity of the proposed method is verified by numerical simulations. Finally, this paper discusses the special case when the magnitude of the thruster force is taken constant. Thrusters can be used for the position and attitude control of satellite systems. For practical satellite systems, the force directions of the thrusters are fixed with respect to the satellite. Sometimes a satellite may be equipped with more than 10 thrusters to control the satellite’s position and attitude. It is obvious that this number of thrusters is more than the minimum necessary to control the satellite’s position and attitude. However, it is not clear how many thrusters are the minimum necessary to control a satellite. The purpose of this study is to clarify the minimum number of thrusters necessary to control the satellite’s position and attitude angle precisely, and to develop the control procedures for a fewer number of thrusters. As a result of this study, we may significantly reduce the number of thrusters for practical satellites, even when considering some of them as backups. Furthermore, the developed control technique is useful when some thrusters have failed. There are many studies dealing with attitude control of satellite systems. Some papers [1]-[7] show an interesting result: “torques about two axes can control the angular velocities and orientation angles about the three axes of a satellite”. These works utilize the non-integrable first-order “nonholonomic” constraints for the attitude motion of the satellites. For the first-order nonholonomic constraints, there are many excellent studies (for examples, References [8]-[13]). On the other hand, the satellite system treated in this study has second-order non-integrable constraints due to the thrusters whose force directions are fixed with respect to the satellites. However, there is much less research [14]-[16] for the second-order nonholonomic constraints than for the first-order systems, and more research is necessary to control the systems. This study is preliminary as it deals with the in-plane motion of a free-floating planar satellite equipped with two thrusters whose force directions are fixed to the satellite. The thrust-level magnitudes of the thrusters are assumed to be continuously changing from zero to a specified positive value. First, this paper shows the general expressions of the system’s equations of motion, and shows that its translational and rotational motions can not be controlled independently. Next, by assuming an imaginary thruster controlled by a feedback law, we transform the nonholonomic constraints into holonomic ones. This concept is followed by a strategy to achieve a rotational motion without drift for a satellite system with two fixed thrusters. Afterwards, this paper shows a procedure for precise control of the position and attitude of the system. The validity of the proposed method is verified by numerical simulations. Finally, this paper discusses the special case when the magnitude of the thruster force is taken constant.

Kinematic discussion and development of a multi-legged planetary exploration rover with an isotropic leg arrangement

This study deals with a multi-legged planetary rover with a spherically isotropic leg arrangement. The legged rover is a reliable rover system for exploration on rough terrains, because it can continue walking even after overturning. Moreover, the legged rover can also show a rotational motion by utilizing its isotropic shape. This paper discusses the walking performance of two types of rover shapes: one has a six-leg arrangement based on a regular octahedron and the other has an eight-leg arrangement based on a regular hexahedron. The design procedure of the proposed rover is explained, and a test-bed system, which is developed to demonstrate the fundamental motions, is also presented.

Comparison of Integrated and Nonintegrated Wide-Field Optic Flow for Vehicle Navigation

Recent studies of vision-based navigation and guidance for robotic vehicles have been inspired by the biological systems found in flying insects. The wide-field integration of optic flow is one pre-existing method, in which the sensed optic flow is integrated along with sensitivity functions to mimic the action of directionally sensitive cells observed in some insects’ visual systems. This study re-examines the wide-field integration method and reformulates the problem from a summation rather than an integral. This reformulation allows the wide-field integration measurement outputs to be directly compared with nonintegrated optic flow measurements. The method using nonintegrated optic flow measurements is shown to have some practical advantages, such as eliminating the need to define input sensitivity functions and having a measurement Jacobian that is easier to derive analytically. Also, the state estimates obtained with the nonintegrated method are proven to have minimum variance compared with those fro...

Considerations on design parameters for attitude control of spacecraft using port-controlled Hamiltonian systems

In previous research, a controller design procedure via generalized canonical transformations has been proposed to keep the passivity feature of Port-controlled Hamiltonian systems. The procedure has a general form and is applicable to spacecrafts attitude motion described with quaternion parameters. This paper investigates the roles of several design parameters in the generalized canonical transformations. Special attention is placed on the relation between the shape of Lyapunov functions and the convergence speed of the state variables. Furthermore, from the analysis utilizing the linearized form of the Port-controlled Hamiltonian system, the guideline to decide the preferable ratio between two parameters in the design procedure is proposed.

Position and attitude control of a planar satellite by two constant force thrusters

This study deals with the in-plane motion of a free-floating planar satellite equipped with two thrusters having constant force magnitude and fixed direction with respect to the satellite. This paper discusses the motion of such a satellite, and proposes a simple trajectory design procedure for controlling both the satellite’s position and attitude angle. First, this paper investigates the motion for constant force magnitude. A drift-less rotational maneuver forms an “invariant manifold”, which can be used to design a trajectory for the target state. Then, the condition of the input profile for the drift-less motion is discussed. Furthermore, this paper explains an advantage of a rotational maneuver which intentionally generates drift velocity.

Interplanetary Trajectory Design of Solar Sail Spacecraft Utilizing an Invariant Manifold

This paper deals with an in-plane trajectory design method for a solar sail spacecraft to rendezvous with a planet. In the interplanetary rendezvous problem, the spacecraft’s velocity must coincide with the orbital velocity of the planet when it reaches the planet’s orbit. This paper proposes a trajectory design procedure that utilizes an invariant manifold for a specified control profile to reach a target orbit. The proposed strategy allows a rendezvous to a planet in an elliptical orbit by adjusting the launch timing of the sailcraft when it starts from a circular orbit. Numerical simulations demonstrate the validity of the proposed procedure.

Considerations on a Feedback Control System for a Space Robot Reorientation

*† This study deals with feedback control of reorientation of a planar space robot. Mukherjee and Kamon propose to define ‘a radially isometric orientation’ and successfully establish a smooth time invariant control system. However the proposed controller suffers from slow rate of convergence for a desired configuration being placed on or near a zeroholonomy curve. They also propose two modified controllers for such configurations, but stability problem for the modified controllers remains future work and a criterion for choosing the original or modified controller is not discussed for general configurations. This paper proposes to adopt a ‘moving desired configuration’ for convergence to any desired configuration. The moving desired configuration is designed to move to a ‘real’ desired configuration with the system states close to an invariant manifold. The paper describes how to define the invariant manifold and how to move the moving desired point to the real one.

An autonomous path planning of a rover utilizing multi-image shape from shading

For planetary exploration, path planning for a rover is one of the important missions. This paper deals with Shape from Shading (SfS) scheme for estimation of planet terrain. As a reliable reflectance model of a surface, the Hapke model is formed in the world of remote sensing. This paper proposes to utilize the Hapke model in the SfS algorithm for multiple camera images. Since the Hapke model has singularity when the gradient vector of a surface element is coincident with a certain direction, the model is modified not to show the singularity. As a result, the SfS algorithm is applicable to multiple camera images and valid regardless of the degree of albedo of the surface. Applying the proposed SfS algorithm for multiple images, an autonomous path planning based on Dynamic Programming is shown. The effectiveness of the proposed scheme is investigated in numerical simulations, and some discussion about the results is presented. INTRODUCTION For planetary exploration, considering the communication time delay between the planet and the earth, the mission is desired to be completed autonomously even in unknown environments. Estimated 3-D elevation map of planetary terrains is very efficient for path planning of rovers. Estimation from camera images is desirable from a point that the images contain terrain information over the region. ’Shape from Shading (SfS)’[1];[2] is one of the most useful techniques because of the simple equipment: a camera and signal processors. However, it has a problem to be solved, the improper convergence of the algorithm caused by Research Associate, member of AIAA y Associate Professor, member of AIAA local minimum, self-shadow, occlusion and noises on camera image. Essentially, estimation of 3-D elevation from only one 2-D camera image is an ’ill-posed’ problem and it has no unique solution. To avoid the problem, it is assumed typically for the standard SfS algorithm that the terrain surface is smooth, and the derivatives of the gradients are minimized. However, the assumption neither be always satisfiable nor improves the results drastically. To utilize multiple camera images for SfS algorithm, the Lommel-Seeliger model[3];[4] has been proposed for the reflection of a surface. However, some experimental results using real camera images are much worse than expected, while the approach can improve the results at least theoretically. One of the most influential factors for the results is improperness of the reflectance model for the albedo of the surface. On the other hand, in the world of remote sensing, the Hapke model[5] [7] is considered as the most reliable reflectance model of a surface. However, the Hapke model shows singularity when the gradient vector of a surface element is coincident with such certain direction that the reflected light angle is close to the incident light angle. Considering that the accuracy for estimated gradient of a surface element is quite low around the singularity, and that 3-D elevation map is produced to put up the surface elements one by one, the inaccuracy caused by the singularity results in unacceptable error. Therefore, this paper proposes to modify the Hapke model and apply the model to the SfS scheme for multiple camera images. First, this paper summarizes the standard SfS algorithm. Then, the explanations for the SfS utilizing multiple images and the reflectance model are followed. Making a comparison with the different models, the modified Hapke model is proposed, which is valid for 1 American Institute of Aeronautics and Astronautics AIAA/AAS Astrodynamics Specialist Conference and Exhibit 5-8 August 2002, Monterey, California AIAA 2002-4825 Copyright