In this paper, a fast and efficient evolutional algorithm, called the G3-PCX has been implemented to solve the forward kinematics problem (FKP) of the general parallel manipulators being modeled by the 6-6 hexapod, constituted by a fixed and mobile platforms being non planar and non-symmetrical. The two platforms are connected by six linear actuators, each of which is located between one ball joint and one universal joint. Forward kinematics are formulated using Inverse Kinematics applying one position based equation system which is converted into an objective function by expressing the sum of squared error on kinematics chain lengths and mobile platform distances. In less than one second, the 16 unique real solutions are computed with improved accuracy when compared to previous methods.

In this paper, the problem of obtaining the optimal trajectory of a Dual-Arm Cam-Lock (DACL) robot is addressed. The DACL robot is a reconfigurable manipulator consisting of two cooperative arms, which may act separately. These may also be cam-locked in each other in some links and thus lose some degrees of freedom while gaining higher structural stiffness. This will also decrease their workspace volume. It is aimed to obtain the optimal configuration of the robot and the optimal joint trajectories to minimize the consumed energy for following a specific task space path. The Pontryagin's Minimum Principle is utilized with a shooting method to resolve kinematic redundancy. Numerical examples are investigated to show optimal trajectories in different cam-locked configurations, and the final decision is made based on a selection table of the computed performance indices.

This paper presents a comparison between control/state estimation methods applied on Par2 parallel manipulator for pick-and-place applications as well as a discussion about the mechanical vibrations issue that may become important when reaching very high accelerations. Real-time experiments were performed first to compare two controllers (a linear Proportional-Derivative controller and a nonlinear/adaptive Dual Mode (DM) controller) complied with the same High-Gain Observer (HGO) to estimate articular velocities, and second to compare three state observers (a Lead-lag-based, an Alpha-beta-gamma (ABG) and an HGO) complied with the same nonlinear DM controller. The stability analysis of the Par2 robot under the control of the proposed DM controller (complied with the HighGO for joint velocity estimation) is also provided. Some small mechanical vibrations were noted when reaching 20 G acceleration, which means that it can become an important issue for higher accelerations. Some suggestions are then made for future investigations to avoid/damp these vibrations.

In this research, using an approximate analytical method, vibration analysis of a 3-PRP (active prismatic—P, passive revolute—R, passive prismatic—P) planar parallel robot having a flexible moving platform is presented. A specific architecture of the 3-PRP parallel robot, also known as the ST (Star-Triangle) parallel robot, is considered. The moving platform of the robot, called the star, is assumed to be made of three flexible beams shaped like a star. For analytical modeling, each of the three beams of the star is assumed to be a discrete Euler–Bernoulli beam with a passive prismatic joint. Continuity equations at the center of the star are used to relate vibrations of the three beams. The vibration behavior of each beam is modeled using previously developed constrained motion equations for a planar Euler–Bernoulli beam having a prismatic joint. In this paper, previously presented “constrained assumed modes method” is further developed to solve the constrained motion equation for the ST parallel robot. The solution method is used to obtain the vibration of the robot for the inverse dynamics problem and simultaneously provides generalized constraint forces. Furthermore, the solution method can be used for the direct dynamics problem of the ST robot. Several input trajectories are considered to investigate the different behavior for the center of the star. For each of the trajectories, three different groups of mode shapes are considered and their vibrational responses are compared. In this research, for the first time, effects of the passive prismatic joint parameters such as mass, rotational moment of inertia, and its actual length are considered in an analytical model. Finally, the analytical solution and a FEM (Finite Element Method) software solution are compared.

Inverse kinematics solutions are the basis for position and orientation control of automated machines in their Cartesian workspace. This paper presents an efficient and robust inverse kinematics algorithm for a new circumferential drilling machine for aircraft fuselage assembly. After a brief introduction to the circumferential drilling machine and its forward kinematics, the paper discusses the nonlinear optimization method for solving inverse kinematics problems. The objective function is defined as a weighted combination of a position error function and an orientation error function. By representing orientation error as the geodesic distance between two points on a unit sphere, the paper proposes to define the orientation error function by using faithful geodesic distance functions, which are accurate approximations to the geodesic distance when it is small. For increased efficiency, robustness, and easy setting of initial values, the inverse kinematics problem is decomposed into two subproblems. The revolute joint coordinates are obtained by nonlinear optimization, and the prismatic joint coordinates are calculated with closed-form formulas. Numerical experiments show that the objective function defined with faithful geodesic distance functions is effective, and the proposed algorithm is efficient, robust, and accurate. The algorithm has been successfully integrated into the control system of the circumferential drilling machine. Preliminary drilling experiments show that the position accuracy of drilled holes is within ±0.5 mm, which is acceptable for the assembly of large aircrafts.

Based on the results of the study of convex object motion1 (J. Hopcroft and G. Wilfong, “Motion of objects in contact,” Int. J. Robot. Res., 4(4), 32–46 (1986)), this paper addresses the problem of exact collision detection of a pair of scaled convex polyhedra in relative motion, and determines the contact conditions of tangential contact features, arbitrary relative motion involving translation and rotation, and uniform scaling of the objects about a fixed point. We propose a new concept of the decision curve based on analytical contact equations that characterize a continuum of scaling factors (or a single scaling factor), which ensures that a pair of objects undergoing a scaling transformation will maintain the same tangential contact feature pair (or make instantaneous tangential contact feature transitions). We propose a reliable simulation-based approach to construct the decision curve by hybridizing analytical contact equations and conventional collision detection method, called the Fast Collision Detection Method (FCDM). This method can determine whether two scaled objects will make contact at specific tangential contact features (vertices, edges, or faces) under particular uniform scaling factors and after distinctive relative motion with better accuracy and less computational time than the existing collision detection methods. Finally, we demonstrate our approach for solving motion design in simple assembly/disassembly problems.

This paper proposes a systematic algorithm based on the concept of interval analysis to obtain the maximal singularity-free circle or sphere within the workspace of parallel mechanisms. As case studies the 3-RPR planar and 6-UPS parallel mechanisms are considered to illustrate the relevance of the algorithm for 2D and 3D workspaces. To this end, the main algorithm is divided into four sub-algorithms, which eases the understanding of the main approach and leads to a more effective and robust algorithm to solve the problem. The first step is introduced to obtain the constant-orientation workspace and then the singularity locus. The main purpose is to obtain the maximal singularity-free workspace for an initial guess. Eventually, the general maximal singularity-free workspace is obtained. The main contribution of the paper is the proposition of a systematic algorithm to obtain the maximal singularity-free circle/sphere in the workspace of parallel mechanisms. The combination of a maximal singularity-free circle or sphere with the workspace analysis by taking into account the stroke of actuators, as additional constraint to the latter problem, is considered. Moreover, the center point of the circle/sphere is not restrained to a prescribed point.

In this paper, based on the Youla-Kucera (Y-K) parameterization, the control of a flexible beam acting as a flexible robotic manipulator is investigated. The method of Youla parameterization is the simple solution and proper method for describing the collection of all controllers that stabilize the closed-loop system. This collection comprises function of the Youla parameter which can be any proper transfer function that is stable. The main challenge in this approach is to obtain a Youla parameter with infinite dimension. This parameter is approximated by a subspace with finite dimensions, which makes the problem tractable. It is required to be generated from a finite number of bases within that space and the considered system can be approximated by an expansion of the orthonormal bases such as FIR, Laguerre, Kautz and generalized bases. To calculate the coefficients for each basis, it is necessary to define the problem in the form of an optimization problem that is solved by optimization techniques. The Linear Quadratic Regulator (LQR) optimization tool is employed in order to optimize the controller gains. The main aim in controller design is to merge the closed-loop system and the second order system with the desirable time response characteristic. The results of the Youla stabilizing controller for a planar flexible manipulator with lumped tip mass indicate that the proposed method is very efficient and robust for the time-continuous instances.

This paper presents a new configuration for ankle rehabilitation using a 9-DOF (degree of freedom) hybrid parallel robot. The robot contains nine linear actuators serially connecting two movable platforms and one stationary platform. The optimization is based on the singularity and dynamic analysis of the robot. The obtained data of the ankle motions from a series of experiments were applied to the model in order to investigate the motion of the end-effector and the force required for each actuator in a particular path. The end-effector tracking simulation results validated the proposed theoretical analysis of the required rehabilitation path of the foot.

A robot working in a hostile environment should be equipped with the necessary risk-avoidance intelligence to survive and accomplish an assigned mission. Covert robotics is a relatively new field in which covert navigation abilities are developed for robots to carry out a mission with minimal potential observation from known or unknown vantage points, with occluding obstacles as the only means of maintaining covertness. The ability to ‘hide’ in order to minimize the risk of being detected is the focus of this paper. A number of strategies are presented that deal with various assumptions about the environment and the hostile observers' locations. The hiding strategies presented for different cases ensure choosing a proper hiding point while taking into account the risk of the chosen path to it.

The Tangent Bundle Rapidly Exploring Random Tree (TB-RRT) is an algorithm for planning robot motions on curved configuration space manifolds, in which the key idea is to construct random trees not on the manifold itself, but on tangent bundle approximations to the manifold. Curvature-based methods are developed for constructing tangent bundle approximations, and procedures for random node generation and bidirectional tree extension are developed that significantly reduce the number of projections to the manifold. Extensive numerical experiments for a wide range of planning problems demonstrate the computational advantages of the TB-RRT algorithm over existing constrained path planning algorithms.

Spinal surgery is considered a high-risk surgery. To improve the accuracy, stability, and safety of such operations, we report the development of a novel six-degrees-of-freedom Robotic Spinal Surgical System that can assist surgeons in performing transpedicular surgery, one of the most common spinal surgeries. After optimization performed using Response Surface Methodology, the largest available workspace of the robot is determined and is found to easily cover the entire operation area. Cooperative control and navigation-based active control are implemented for different processes of the operation. We propose a hybrid control approach based on the speed and torque interface at the joint level. In this mode, the robot is compliant in Cartesian space, benefitting both the accuracy and efficiency of the operation. A comprehensive assessment index, combining the subjective and objective criteria in terms of positioning and operation efficiency, is proposed to compare the performance of cooperative control in speed mode, torque mode, and hybrid control mode. Active fine adjustment experiments are carried out to verify the positioning accuracy, and the results are found to satisfy the requirements of operation. As an application example, a pedicle screw insertion experiment is performed on a pig vertebral bone, demonstrating the effectiveness of our system.