Shabbir Kurbanhusen Mustafa

Self-Calibration of a Biologically Inspired 7 DOF Cable-Driven Robotic Arm

This paper presents the self-calibration of a novel biologically inspired 7 DOF cable-driven robotic arm. Similar to the human arm, the proposed robotic arm consists of three sequentially connected modules, i.e., a 3 DOF shoulder module, a 1 DOF elbow module, and a 3 DOF wrist module. Due to factors like manufacturing defects, assembly misalignments, compliance, and wear of connecting mechanisms, errors in the geometric model parameters always exist. Hence, the identification of such errors is critical for path planning and motion control tasks. Self-calibration models of the various modules in the robotic arm are formulated based on the differential change in the cable end-point distances. Due to the linear nature of these self-calibration models, an iterative least-squares algorithm is employed to identify the errors in the geometric model parameters. The calibration does not require any external pose measurement devices, because it utilizes the cable length data obtained from the redundant actuation scheme of the cable-driven arm. Computer simulations and experimental studies were carried out on both the 3 DOF and 1 DOF modules, to verify the robustness and effectiveness of the proposed self-calibration algorithm. From the experimental studies, errors in the geometric model parameters were precisely recovered after a minimum number of pose measurements.

On the Force-Closure Analysis of n-DOF Cable-Driven Open Chains Based on Reciprocal Screw Theory

It has been mathematically proven that a completely restrained n- degree-of-freedom (n-DOF) single rigid-bodied cable-driven platform requires a minimum of n + 1 cables with positive tension to fully constrain it. However, the force-closure analysis of open chains that are driven by cables is still an open question. For the case of an n -DOF cable-driven open chain, the following two important questions arise. 1) How can the force-closure analysis be carried out for a given cable routing configuration, while retaining the geometric insights of the problem? 2) Are n + 1 cables sufficient to fully constrain the entire chain? This paper addresses these issues by proposing a systematic and novel approach based on the reciprocal screw theory. The key idea is to express wrenches acting on the open chain as linear combinations of the reciprocal screws and determine the total required torques at each joint. This is followed by equating the joint torques that are provided by the cable forces with the joint torques, which are required by the external wrenches, and checking for force closure. The proposed methodology can analyze open chains with arbitrary cable routing configuration. The analysis shows that the entire n-DOF open chain requires a minimum of n + 1 cables to fully constrain it.

A geometrical approach for online error compensation of industrial manipulators

In this paper, a comprehensive online error compensation approach using offline calibration results is proposed for industrial manipulators (with closed control architecture), in order to improve its accuracy. The contents in this paper include a calibration algorithm based on the product-of-exponential formula, an online error compensation procedure for implementing the calibration results on industrial manipulators, and an experimental study that is conducted on a 6-DOF industrial manipulator from ABB (Model: IRB-4400) with a laser tracker system from Leica (Model: AT901-MR) and its Tracker-Machine control sensor. After implementing the proposed online error compensation approach, the accuracy of the ABB industrial manipulator improved to 0.3 mm, thus verifying the effectiveness of the proposed error compensation approach.

Numerical Orientation Workspace Analysis with Different Parameterization Methods

For numerical orientation workspace analysis, a finite partition of the orientation workspace in its parametric domain is necessary. Among various parameterization methods for rigid-body rotations, it has been realized that the Euler angles, the tilting-and-torsion (T&T) angles, and the exponential coordinates are appropriate for finite partition. With these three parameterization methods, the rigid body rotation group, i.e., the special orthogonal group (SO(3)), can be mapped to a rectangular parallel-piped (for Euler angles), a solid cylinder (for T&T angles), and a solid sphere (for exponential coordinates). To simplify the computation, isotropic/equi-volumetric partition schemes are proposed for the three geometric entities so that each of them can be geometrically divided into finite elements with equal volumes. As a result of parameterizations, the volume of orientation workspace, i.e., the volume of SO(3), can be numerically computed as a weighted volume sum of its constituent equi-volumetric elements in which the weightages are the element associated integration measures. Using such partition schemes, various global performance measures can be readily implemented so as to evaluate the quality of the orientation workspace. A comparison study for the three parameterization methods has shown that the exponential coordinates method is more effective for numerical orientation workspace analysis because it has no formulation singularity and exhibits higher computation accuracy

A generic tension-closure analysis method for fully-constrained cable-driven parallel manipulators

Cable-driven parallel manipulators (CDPMs) are a special class of parallel manipulators that are driven by cables instead of rigid links. Due to the unilateral property of the cables, all the driving cables in a fully-constrained CDPM must always maintain positive tension. As a result, tension analysis is the most essential issue for these CDPMs. By drawing upon the mathematical theory from convex analysis, a sufficient and necessary tension-closure condition is proposed in this paper. The key point of this tension-closure condition is to construct a critical vector that must be positively expressed by the tension vectors associated with the driving cables. It has been verified that such a tension-closure condition is general enough to cater for CDPMs with different numbers of cables and DOFs. Using the tension-closure condition, a computationally efficient algorithm is developed for the tension-closure pose analysis of CDPMs, in which only a limited set of deterministic linear equation systems need to be resolved. This algorithm has been employed for the tension-closure workspace analysis of CDPMs and verified by a number of computational examples. The computational time required by the proposed algorithm is always shorter as compared to other existing algorithms.

Development of a Bio-Inspired Wrist Prosthesis

This paper presents a novel mechanical design of a 3-DOF wrist prosthesis. Mimicking biological solutions from the human arm anatomy, the wrist prosthesis is designed to have a parallel structure and is cable-driven. This results in a much lighter prosthesis, with higher loading capacity as compared to a rigid-linked, serial structured design. Based on the wrist joint capabilities, this paper focuses on the cable tension, stiffness and workspace analyses. This is to develop a comprehensive framework to optimize the wrist prosthesis design. Finally, a prototype is fabricated based on the optimization results

Kinematic analysis and design optimization of a cable-driven universal joint module

Cable-driven parallel manipulators (CDPMs) are a special class of parallel manipulators that are driven by cables instead of rigid links. So CDPMs have a light-weight structure with large reachable workspace. The aim of this paper is to provide the kinematic analysis and the design optimization of a cable-driven 2-DOF module, comprised of a passive universal joint, for a reconfigurable system. This universal joint module can be part of a modular reconfigurable system where various cable-driven modules can be attached serially into many different configurations. Based on a symmetric design approach, six topological configurations are enumerated with three or four cables arrangements. With a variable constrained axis, the structure matrix of the universal joint has to be formulated with respect to the intermediate frame. The orientation workspace of the universal joint is a submanifold of SO(3). Therefore, the workspace representation is a plane in R2. With the integral measure for the submanifold expressed as a cosine function of one of the angles of rotation, an equivolumetric method is employed to numerically calculate the workspace volume. The orientation workspace volume of the universal joint module is found to be 2π. Optimization results show that the 4-1 cable arrangement produces the largest workspace with better Global Conditioning Index.

Tension optimization for cable-driven parallel manipulators using gradient projection

Cable-driven parallel manipulators (CDPMs) are a special class of parallel manipulators that are driven by cables instead of rigid links. Cables have unilateral driving properties so that redundant actuation is required to maintain positive cable tensions. Due to the actuation redundancy, there exists an infinite number of tension solutions for every CDPMs pose. In this paper, a gradient projection method is employed for tension optimization of CDPMs. This optimization process minimizes a performance criterion which is a function of the cable tensions and the tension limits. The steepest descent direction of the performance criterion is projected onto the null space of the structure matrix to provide the direction towards the local minimum. Global optimal tension solution is found by repeating this process. A factor is introduced to adjust the tension solution towards the upper or lower tension limits. Simulation results show that the algorithm produces tension solutions that are continuous and smooth.

Self-calibration of a biologically-inspired cable-driven robotic arm

Identification of errors in the geometric model parameters of a robotic arm is critical for path planning and motion control. This paper presents the self-calibration of a novel biologically-inspired cable-driven robotic arm. A self-calibration model is formulated based on the differential change in the cable end-point distances. A computationally efficient algorithm using iterative least-squares is employed to identify the errors in the geometric model parameters. It does not require any external measurement devices because it utilizes the cable length data obtained from the redundant actuation scheme of the cable-driven arm. Both computer simulations and experimental studies were carried out to verify the robustness and effectiveness of the proposed self-calibration algorithm. From the experimental studies, errors in the geometric model parameters were precisely identified after a minimum of 35 pose measurements.

Reciprocal screw-based force-closure of an n-DOF open chain: Minimum number of cables required to fully constrain it

Due to the unilateral driving property of cables, it has been mathematically proven that a 6-DOF single rigid-bodied cable-driven platform requires a minimum of 7 cables with positive tension to fully constrain it. However, force-closure analysis of open chains driven by cables is still an open question. For the case of an n-DOF open chain driven by cables, two important questions arise: (i) Are n+1 cables sufficient to fully constrain the entire chain? (ii) How can force-closure analysis be carried out for a given cable routing configuration while retaining the geometric insights of the problem? This paper will address these issues and propose a systematic and novel approach based on the reciprocal screw theory. The analysis shows that the entire n-DOF open chain requires a minimum of n+1 cables to fully constrain it and the proposed methodology can analyze any cable routing configuration.