Anirvan DasGupta

Impedance Control of Space Robots Using Passive Degrees of Freedom in Controller Domain

Impedance control is an efficient and stable method of providing trajectory and force control in robotic systems. The procedure by which the impedance of the manipulator is changed is a very important aspect in the design of impedance based control schemes. In this work, a scheme is presented in which the control of impedance at the interface of the end effector and the space structure is achieved by introduction of a passive degree of freedom (DOF) in the controller of the robotic system. The impedance is shown to depend upon a compensation gain for the dynamics of the passive DOF. To illustrate the methodology, an example of a two DOF planer space robot is considered.

A scheme for robust trajectory control of space robots

Abstract This paper presents a scheme for robust trajectory control of free-floating space robots. The idea is based on the overwhelming robust trajectory control of a ground robot on a flexible foundation and robust foundation disturbance compensation presented elsewhere. No external jets/thrusters are required or used in the scheme. An example of a three-link robot mounted on a free-floating space platform is considered for demonstrating the efficacy of the control scheme. Bond graph technique has been used for the purpose of modeling and simulation. Robustness of the control scheme is guaranteed since the controller does not require the knowledge of the manipulator parameters.

KINEMATICS OF FLOWS ON CURVED, DEFORMABLE MEDIA

Kinematics of geodesic flows on specific, two-dimensional, curved surfaces (the sphere, hyperbolic space and the torus) are investigated by explicitly solving the evolution (Raychaudhuri) equations for the expansion, shear and rotation, for a variety of initial conditions. For flows on the sphere and on hyperbolic space, we show the existence of singular (within a finite value of the time parameter) as well as non-singular solutions. We illustrate our results through a phase diagram which demonstrates under which initial conditions (or combinations thereof) we end up with a singularity in the congruence and when, if at all, we can obtain non-singular solutions for the kinematic variables. Our analysis portrays the differences which arise due to positive or negative curvature and also explores the role of rotation in controlling singular behavior. Subsequently, we move on to geodesic flows on two-dimensional spaces with varying curvature. As an example, we discuss flows on a torus. Characteristic oscillatory features, dependent on the ratio of the two radii of the torus, emerge in the solutions for the expansion, shear and rotation. Singular (within a finite time) and non-singular behavior of the solutions are also discussed. Finally, we conclude with a generalization to three-dimensional spaces of constant curvature, a summary of some of the generic features obtained and a comparison of our results with those for flows in flat space.

Kinematics of geodesic flows in stringy black hole backgrounds

We study the kinematics of timelike geodesic congruences in two and four dimensions in spacetime geometries representing stringy black holes. The Raychaudhuri equations for the kinematical quantities (namely, expansion, shear, and rotation) characterizing such geodesic flows are written down and subsequently solved analytically (in two dimensions) and numerically (in four dimensions) for specific geodesic flows. We compare between geodesic flows in dual (electric and magnetic) stringy black hole backgrounds in four dimensions, by showing the differences that arise in the corresponding evolutions of the kinematic variables. The crucial role of initial conditions and the spacetime curvature on the evolution of the kinematical variables is illustrated. Some novel general conclusions on caustic formation and geodesic focusing are obtained from the analytical and numerical findings. We also propose a new quantifier in terms of the time (affine parameter) of approach to a singularity, which may be used to distinguish between flows in different geometries. In summary, our quantitative findings bring out hitherto unknown features of the kinematics of geodesic flows, which, otherwise, would have remained overlooked, if we confined ourselves to only a qualitative analysis.

Kinematics of deformable media

Abstract We investigate the kinematics of deformations in two and three dimensional media by explicitly solving (analytically) the evolution equations (Raychaudhuri equations) for the expansion, shear and rotation associated with the deformations. The analytical solutions allow us to study the dependence of the kinematical quantities on initial conditions. In particular, we are able to identify regions of the space of initial conditions that lead to a singularity in finite time. Some generic features of the deformations are also discussed in detail. We conclude by indicating the feasibility and utility of a similar exercise for fluid and geodesic flows in a flat and curved spacetimes.

Impedance Control of Space Robot

Abstract The force control of a space robot is a difficult task, as the interaction of robot tip with the environment causes the base to change its position and orientation. Impedance control is an efficient method for trajectory and force control in a robotic system. The procedure by which the impedance of the manipulator is changed is a very important aspect in the design of impedance-based control schemes. This paper presents a scheme in which the control of impedance at the end-effector environment interface is achieved by introduction of a passive degree of freedom (DOF) in the robotic system in the controller. The impedance depends upon a gain compensation for the dynamics of the passive DOF.

Attitude Control of a Free-Flying Space Robot using a Novel Torque Generation Device

In this paper we present a new torque generation device that can be used to control the attitude of space robots. The device is based on the principle of continuously variable transmission. A detailed analytical study of the device has been performed, and the behavior and stability of the overall system have been studied. Bond graph modeling has been used to conceive the device. The advantage of using this device is that many control strategies are possible for the control of a space vehicle.

A Methodology for Finding Invariants of Motion for Asymmetric Systems with Gauge-Transformed Umbra Lagrangian Generated by Bond Graphs

The purpose of this article is to obtain conservation laws (invariants of motion) for different energy domains through the extended Noether theorem and bond graphs. Bond graphs are profitably used in representing the physics of a system as well as obtaining its umbra-Lagrangian. The article extends Lagrangian-Hamiltonian mechanics to deal with asymmetries in the system, which incorporates dissipative and nonpotential fields in a compact Lagrangian form, such that one may obtain invariants of motion through extension of Noether’s theorem. A detailed methodology is outlined in this article for obtaining the invariants of motion for a general class of asymmetric systems with a gauge-transformed umbra-Lagrangian. Symmetrization of an asymmetric system is introduced through the concept of gauge functions, for which the classical Noether theorem is extended over vector fields in the extended manifold comprising real and umbra displacements and velocities, as well as real time. A generalization of the variational principle or least action principle is also presented, which leads to the proposed form of the umbra-Lagrange equation through recursive minimization of functionals. Several illustrative examples are given to elucidate this concept in different physical contexts.

Geodesic congruences in warped spacetimes

In this article, we explore the kinematics of timelike geodesic congruences in warped five-dimensional bulk spacetimes, with and without thick or thin branes. Beginning with geodesic flows in the Randall-Sundrum anti-de Sitter geometry without and with branes, we find analytical expressions for the expansion scalar and comment on the effects of including thin branes on its evolution. Later, we move on to congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using analytical expressions for the velocity field, we interpret the expansion, shear and rotation (ESR) along the flows, as functions of the extra dimensional coordinate. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observers point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in backgrounds with a thick brane are solved numerically in order to figure out the role of initial conditions (prescribed on the ESR) and spacetime curvature on the evolution of the ESR.

Geodesic flows in rotating black hole backgrounds

We study the kinematics of timelike geodesic congruences, in the spacetime geometry of rotating black holes in three (the BTZ) and four (the Kerr) dimensions. The evolution (Raychaudhuri) equations for the expansion, shear and rotation along geodesic flows in such spacetimes are obtained. For the BTZ case, the equations are solved analytically. The effect of the negative cosmological constant on the evolution of the expansion (