Sandipan Bandyopadhyay

The 3-RRS parallel manipulator presented in this study comprises of parallel revolute joint axes in each leg. The manipulator is composed of a base and a moving platform which are in the shape of equilateral triangles. Moving platform has two rotational and one translational degrees-of-freedom. This study formulates the forward and inverse kinematics of the parallel manipulator. A 16th order polynomial in terms of one of the passive joint variables is obtained for the forward kinematic analysis. Numerical results and the corresponding pose of the manipulator for inverse and forward kinematics are presented.

A new strategy for the design of tracking control laws is presented for line-of-sight (LoS) pointing control of satellites that use only magnetorquers. This strategy makes use of the backstepping approach, and applies to satellites that require the LoS of a single instrument, such as a transmission antenna or camera, to be pointed at a given time, but not both simultaneously. Asymptotic stability of the desired trajectory is proved, provided the target pointing-direction lies outside some critical range. A control law so developed is numerically simulated for a nanosatellite mission scenario to demonstrate feasibility. © 2013 2013 California Institute of Technology.

This paper presents some analytical results related to the determination of the singular poses of the 3-RPS parallel manipulator at which it gains two degrees of freedom. The forward kinematic univariate (FKU) of the manipulator acquires a special structure at such a pose. All such poses have been identified in the closed-form, using a Stüdy-parameter representation of SE(3), for both the operation modes of the 3-RPS. These results are novel, to the best of the knowledge of the authors, and these have been verified using the traditional method, using the criterion of loss of rank of certain Jacobian matrices. The theoretical results have been illustrated with numerical examples.

This paper proposes a deterministic estimator for the estimation of the attitude of a rigid body. A deterministic estimator uses a minimal set of information and does not try to minimize a cost function or fit the measurements into a stochastic process. The proposed estimator obtains the attitude estimation utilizing only the properties of the rotational group SO(3). The information set required by the proposed estimator is a single vector information and rate gyro readings. For systems in which one of the rotational freedom is constrained, the proposed estimator provides an accurate estimate of the reduced attitude. The performance of the algorithm is verified on different experimental testbeds.

This paper presents a methodology to synthesise mechanisms free of kinematic defects in precision-point problems. The considerations for obtaining defect-free mechanisms are embedded in the mathematical formulation of the exactsynthesis procedure. However, this requires that at least one less target point is specified than the maximum number that the mechanism can reach exactly. An example from the existing literature of a four-bar linkage is studied. Identification of the branch-transition and the circuit-transition linkages enables the characterisation of the feasible ranges of the solutions in the design parameter space. These linkages are identified by formulating appropriate systems of polynomial equations and solving them. A root-generation algorithm reported in literature called cyclic coefficient-parameter continuation is employed to establish the finite root-count of these systems. Once the kinematic defect-free branch/circuit-transition linkages are identified, other design objectives can be brought into consideration to find optimal solutions in the feasible design ranges using design parameter continuation starting with these linkages. The results obtained demonstrate certain advantages afforded by proposed methodology over the existing exact and optimal methods for the synthesis of mechanisms.

The presence of backlash in the gearheads is an inherent problem in manipulators using geared motors. This paper looks at a potential solution to this problem via the implementation of a dual-loop control strategy, in which feedback is taken from the motors as well as the end-effector of the manipulator. Using the redundant sensed information, the actual error in the joint-space is computed and used to rectify the desired trajectory for the joint-space trajectory-tracking control scheme. Experiments done on a 3-RRR planar parallel manipulator show significant improvement in the tracking performance due to the introduction of dual-loop control scheme.

This paper presents a comparative study between two related methods of formulating the equations of motion, within the Lagrangian framework, for closed-loop mechanisms. Such mechanisms encounter singularities not only at the boundaries of their workspaces, but also inside the workspaces. The latter kind of singularities are detrimental to the operation of the mechanisms and may lead to their mechanical failure. The primary objective of the paper is to investigate the ways in which these singularities impact the two formulations, and to establish a relation between them. A planar five-bar mechanism is used to illustrate that the singularities appearing in one formulation is a subset of those appearing in the other formulation. The second objective is to provide a qualitative analysis of the time-complexities of the respective formulations. A planar five-bar and the Stewart platform manipulator are used to study and compare the computational costs incurred in either of the formulations.

This paper presents a novel analytical formulation for identifying the closest pair of points lying on two arbitrary cylinders in space, and subsequently the distance between them. Each cylinder is decomposed into four geometric primitives. It is shown that the original problem reduces to the computation of the shortest distance between five distinct combinations of these primitives. Four of these subproblems are solved in closed form, while the remaining one requires the solution of an eight-degree polynomial equation. The analytical nature of the formulation and solution allows the identification of all the special cases, e.g., positive-dimensional solutions, and the curve of intersection when the cylinders interfere. The symbolic precomputation of the results leads to a fast numerical implementation, capable of solving the problem in about 50 ls (averaged over 1×106 random instances of the most general case) on a standard PC. The numerical results are verified by repeating all the calculations in a general-purpose commercial CAD software. The algorithm has significant potential for applications in the various aspects of robotics and mechanisms, as their links can be modeled easily and compactly as cylinders. This makes tasks such as path planning, determination of the collision-free workspace, etc., computationally easier.

The planar 3-RRR parallel manipulator is known to have six assembly modes. However, analysing it in the framework of spatial kinematics reveals that it has a total of twelve assembly modes, six in each of the two possible operation modes. The modes are derived using a Study parameter formulation first, and later confirmed in another formulation in the joint-space, and finally visualised in terms of the planar constraint curves generated by the sub-chains of the manipulator. Numerical results show that all the twelve modes can be real for certain inputs.

This paper presents a method to compute the largest possible cylindrical volume within the translational workspace of the semi-regular Stewart platform manipulator (SRSPM), which would be free of gain-type singularities. An analytical approach is used in finding the singularity-free regions rather than discretising the workspace into small singularity-free volumes. Comparison with another convex shape, i.e., the sphere, is performed to demonstrate the relative importance and usefulness of using the cylindrical geometry for finding the singularity-free spaces.