Human & Robot Interaction Lab. (TaarLab)

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In TaarLab, parallel robots are investigated under different perspectives. Different studies are conducted on this regard. Since extensive studies have been carried out in the literature on such a robot thus more emphasis is placed on applying novel optimization approach, such as interval analysis and convex optimization, to the end of designing the most promising one in term of kinematic and dynamic properties. Topics under investigation for parallel robots can be summarized as:


Collision-Free Workspace Determination via Triangle-to-Triangle Intersection Test

People Involved
   Behzad Danaei and Nima Karbasizadeh

This project introduces a new general systematic approach, which is based on the so-called triangle-to-triangle intersection test, in order to obtain the collision-free workspace of robotic mechanical systems. In the proposed geometric constructive approach, a collision test will be performed on the STL file for all possible configurations of the robot which leads to obtaining the collision-free workspace. In this approach, by introducing a bounding sphere, from the obtained results it reveals that the computational time on average is 0.049 μs per test which is reduced by 23% comparing to one of the recent algorithm proposed in the literature. Furthermore, the collision-free workspace determination approach provides a statistical data about the percentage of collision for each constituting part of the mechanism. By resorting to the latter statistical data, an index for collision-free workspace is introduced which provides some insights into designing a well-conditioned workspace in terms of mechanical interference.

Collision free workspace of 3 RRR parallel mechanism
Collision-free workspace of 3-RRR parallel mechanism.

A 3 RRR planar manipulator meshed with triangles in STL file
A 3-RRR planar manipulator meshed with triangles in STL file.

Dynamic modeling and base inertial parameters determination of 2-DOF TezGoz

People Involved
   Behzad Danaei and Alaleh Arian

This project deals with the dynamic modeling and base inertial parameter determination of a general 5R 2-degree-of-freedom spherical parallel manipulator. By using a new geometric approach, inverse and forward kinematic problem are transformed to the problem of determining the intersection of two cones with common vertex. Compared to other proposed methods, this approach yields more compact and closed-form solutions. The instantaneous kinematic and acceleration problem is solved via employing the screw theory. The dynamic model is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. In order to verify the proposed methods and equations, a case study is performed, in which an orthogonal 2-DOF SPM, named TezGoz, is considered. Performed simulations and comparisons with a SimMechanics model show the correctness of the derived equations. Furthermore, a reduced dynamic model is obtained by determining the base inertial parameters. To do so, first the dynamic model is rewritten in a linear matrix form with respect to the inertial parameters of the mechanism, then parameters are grouped to obtain a set of independent base parameters, reducing the number of inertial parameters from 40 to 19. As a result, while maintaining the accuracy, the computational time is reduced to 63% of that of the original dynamic model. Finally, to calibrate the dynamic model, an experimental dynamic identification is performed.

A general 5R spherical parallel manipulatorA general 5R spherical parallel manipulator.

The TezGoz spherical parallel manipulatorThe TezGoz spherical parallel manipulator

Kinematic and Dynamic Analysis of a 3-DOF Translational Parallel Manipulator

People Involved
   Behzad Danaei and Alaleh Arian

In this research, as the main contribution, a comprehensive study is carried out on the mathematical modeling and analysis of the inverse kinematics and dynamics of an over-constraint three translational degree-of-freedom parallel manipulator. Since dynamic formulation of over-constraint parallel manipulators do not admit solution, due to the inconsistency between the number of equations and unknowns, thus the problem has initiated many challenges. In order to obtain a dynamical model, and circumvent the problem of inconsistency between the number of equations and unknowns, a modification is applied in the kinematic arrangement of the under study manipulator by preserving the performed motion pattern. Then, the dynamical equations of the manipulator are obtained based on the Newton–Euler approach and a simple and compact formulation is provided and all the joint forces and torques are presented. In order to evaluate the accuracy of the obtained formulated model, a motion for the end-effector as case study is performed, and it has been shown that the results of the analytical model are in good agreement with those obtained from SimMechanics model.

Vector notation for the kinematic modeling of the TripteronVector notation for the kinematic modeling of the Tripteron.

Free body diagram of the under study manipulator afterFree-body diagram of the Tripteron manipulator

Singularity-free workspace of PMs using interval analysis and geometrical approach

People Involved
   Mohammad Hadi Farzaneh Kaloorazi and  Stephane Caro

 The presence of the singular configuration in the workspace of the parallel robots is a major deterrent to widespread of PMs in the industrial context. Therefore, these configurations must be avoided. There are many techniques addressed in the literature in order to obtain and avoid the singularity. Many of these techniques are applicable only in specific cases. In this project first, a novel approach is proposed to obtain the singularity expression of parallel robots using screw theory and geometric properties of singular configurations. Then, resorting to interval analysis, the branch and prune algorithm to obtain the workspace of robots is represented. A novel approach to obtain the maximal singularity-free circle/sphere in the workspace of planar PMs, such as 3-RPR, and spatial PMs, such as 6-UPS. The singularity-free workspace insures the application of the robot in aforementioned workspace. 


Collision-free Workspace of Parallel Mechanisms Using Interval Analysis

People Involved
   Mohammad Hadi Farzaneh Kaloorazi, Stephane Caro

 This project proposes an interval-based approach, to obtain the collision-free workspace of planar parallel mechanisms. This approach is represented through an example for a 3-RPR planar parallel mechanism and 6-UPS spatial parallel mechanisms. Three main feature of the collision-free workspace is taken into account: mechanical stroke of actuators, interference of limbs with the obstacle and interference of end-effector with the obstacle. In this project, a circle shaped obstacle is considered and its mechanical interference with limbs and edges of the end-effector is taken into account.


A Geometric Constructive Approach for Singularity-free Workspace of PMs

People Involved
   Mohammad Hadi Farzaneh Kaloorazi and Stephane Caro


This project proposes a novel approach to obtain the  maximal singularity-free regions of planar parallel mechanisms which is based on a constructive geometric reasoning. The proposed approach consists of two algorithms. First, the borders of the  singularity-free region corresponding to an arbitrary start point of the moving platform is obtained. Then, the second algorithm aims to find the center of the maximal singularity-free circle which is obtained using the so-called offset curve algorithm.  As a case study, the procedure is applied to a  3-PRR planar parallel mechanism and results are given in order to graphically illustrate the effectiveness of the proposed algorithm. The proposed approach can be directly applied to obtain the maximal singularity-free circle of similar parallel mechanisms, which is not the case for other approaches proposed in the literature which is limited to a given parallel mechanism, namely, 3-RPR. Moreover, as the main feature of  the proposed approach, it can be implemented both in a CAD system or in a computer algebra system where non-convex and re-entrant curves can be considered.


Workspace Determination of PMs with Progressive Growing Neural Gas Network (PGNGN)

People Involved
   Roya Sabbagh NovinMojtaba Yazdani


In the most of the works for implementation and control of parallel robots, especially Generally, in parallel robots, solving the forward kinematic problem is much harder than finding the inverse kinematic solution, thus, workspace determination using FKP is a demanding task in most cases. Therefore, in this research, a progressive growing neural gas network algorithm (PGNGN) is proposed, which is a systematic and general approach to obtain the topology of the workspace based on IKP equations.

After establishing a preliminary network with few initial data points, the network starts to develop itself by considering new data points around its border neurons through a boundary data generation procedure.
The proposed algorithm is able to continue learning, adding units and connections, until a performance criterion has been met which leads to a clear workspace topology with minimal errors.

The most important features of this algorithm are the abilities to detect cavities in the workspace, consider singularities and distinguish separated regions of the workspace. Till now, workspace of various parallel robots including 3-RRR, 3-RPR and 3-PRR mechanisms and a Gouph-Stewart platform have been determined. Results reveal the applicability and reliability of this method.

Then upon apply different levels of input voltage on the actuator, different step responses are studied in the presence of dead zone, delay and saturation. Through a linear identification process, a nominal second-order linear model is estimated for the actuator. Based on the identified model, the position (length) of the actuator is controlled by applying some straightforward and reliable control solutions.


Workspace Determination of a 3-DOF Parallel Robot Considering Joint Limits

People Involved
   Mojtaba Yazdani, Roya Sabbagh Novin

Workspace analysis is one of the most important steps in the procedure of designing industrial robots. The workspace of a robot is defined as the set of all end-effector configurations which can be reached by some choice of joint coordinates.

Various approaches may be used to calculate the workspace of a parallel robot which can be classified by geometrical approaches, discretization method and numerical procedures.

The main features of the geometrical approaches are their fastness and accuracy, which are necessary in efficient calculation of some characteristics of the workspace, such as volume. Moreover, all mechanical and kinematic constraints can be considered using this method.

Using SolidWorks software, the workspace of a 3-DOF decoupled parallel robot, developed in TaarLab, is determined, considering all joint limits and mechanical interface of joints. Since all DOFs are transitional the resulting area is an appropriate representation of the workspace.


Design, Development and Dynamic Simulation of a 2-DOF Spherical PM

People Involved
   Mojtaba Yazdani, Amirhossein KarimiIman Yahaypour, Esmaeil Rostami

Spherical manipulators is a class of manipulators that can orient the end-effector about the center of rotation of the mechanism. The developed mechanism in this project performs as same as a human eye with a larger workspace. This mechanism can be employed in position tracking systems, such as object tracking cameras and antenna or solar tracker systems.

This mechanism benefits from two AX-12 Dynamixel actuators which are both fixed to the base. All arms of the robot are designed in order to minimize the moving inertia of the mechanism to increase its agility. In each R-joint, four SKF-618 series bearings are used to ensure the alignment and sufficient stiffness of the joints. Recently, a wireless camera installed in the center of the end-effector is replaced with a higher fps PS4 camera to enhance the tracking performance of the robot.

The dynamic analysis used in this project is based on a judicious concept in detaching the whole mechanism into several subsystems and consecutive synergies between kinematic analysis, Lagrangian and Newtonian approaches. The proposed approach performance for the dynamics of this mechanism is analyzed by means of several test trajectories for the end-effector and the results are put into contrast by the ones obtained with a dynamic analyzer software. Then, a co-simulation between MATLAB and MD-Adams has been accomplished in order to control this mechanism via computed torque method. The latter method has led the end-effector to follow the desired trajectory.

Finally, it should be noted that all image processing and object tracking codes are generated in C++ developed by QT Creator IDE by other members of the project.

aigle2  AgileEye2DoF

Design, Development and Dynamic Simulation of a 3-DOF Spherical PM

People Involved
   Mojtaba Yazdani, Iman Yahaypour, Milad Hasanvand

Spherical parallel manipulators have great advantages in their agility and stiffness. In this project, a 3-DOF spherical parallel manipulator is designed based on Agile Eye 3-DOF from Laval University. In TaarLab version, each R-joint contains four SKF-618 series bearings to ensure the alignment and sufficient stiffness of the joints.

Three Dynamixel actuators from MX series with good force control performance are used in order to use this robot in haptic applications like Lasik surgery on eyes and virtual dentistry training. Another main application of this spherical manipulator is in position tracking systems as previously mentioned about the 2-DOF one.

The dynamic modeling approach used in this project is based on detaching the manipulator into several subsystems and applying a consecutive synergy between kinematic analysis, Lagrangian and Newtonian approaches. In this regard, the manipulator under study is detached to four subsystems. After writing down the kinematic equations of all the three subsystems, the Lagrangian and Newtonian approaches are blended and finally the dynamic model of the manipulator is obtained. Finally, the problem leads to a system of 12 equations and 18 unknowns, which has been simplified to have a fully constraint system of equations.
The results are put into contrast by the one obtained with an analyzer software, MDAdams. Then, a co-simulation between MATLAB and MD-Adams has been accomplished in order to control the manipulator with computed torque control method. The latter method has led to the end-effector to follow the desired trajectory perfectly.

aigle3 1 

Design, Development and Dynamic Simulation of Triptron

People Involved
   Mojtaba Yazdani, Pourya Shahverdi, Navid Kashi, Iman Yahaypour

Parallel manipulators play a very important role in pick and place tasks in robotic industries due to their precision and high velocities. In this project which is funded by the INSF, a new configuration of Tripteron which is a 3-DOF fully-decoupled firstly built in Laval University is developed in order to increase its workspace and acceleration.

The manipulator contains three PRRR structure limbs with fixed-base actuators. This let us use powerful 1.2 KW BONMET AC Servo actuators with great control performance. All moving parts are made of AL 7075-T6 alloy to increase the stiffness and reduce the moving inertia of the mechanism and precise linear modules are used as active the prismatic joints.

Based on the application, various tools or parts could be attached to the end-effector of the manipulator such as a pneumatic gripper. Due to the high acceleration of the manipulator, it also could be used as a test platform to do functional test of product in high acceleration. Moreover, since the actuator perform well in force feedback control, this mechanism also could be used as a haptic rehabilitation system.
The reasoning used in dynamic modeling of the manipulator is based on a judicious concept in detaching the whole mechanism into several subsystems and consecutive synergies between kinematic analysis, Lagrangian and Newtonian approaches.


Design and Development of a Pneumatic 6-DOF Gough-Stewart

People Involved
   Mojtaba Yazdani, Milad Hasanvand, Jalal Haji Pour Machiani, Foad Saniei

This robot is developed in order to have an experimental platform to simulate 6-DOF motions of dynamic systems such as driving and flight simulators.

Developed platform has six links and each link contains one linear potentiometer, for the exact position of link, two pressure indicators, for input and output pressures of the jack, and one valve to adjust the air flow. These actuators were connected to the base with spherical or universal joints. The orientation and position of the moving platform are given and using Inverse Kinematic Problem (IKP) trying to obtain the length of each link. Then air flow rate of each valve and rate of air pressure passing over each cylinder have been modeled based on displacement of each piston.

The reason for using Gough-Stewart platform as a flight simulator is mainly due to its high capability of load transferring. Moreover, high precision positioning is another advantage. Actuators are commonly under tension or compression forces rather than bending which results less deformation in them.
In the most of the works for implementation and control of parallel robots, especially Gough-Stewart platform utilize electrical servo motors or force sensor and less attention has been paid to pneumatic actuators. Pneumatic actuators are favored because they have low weight, small size, high load operation and the possibility to use directly. Moreover, their cost is up to 20 percent less than electrical actuators and operating frequency is considerably higher than hydraulic actuators. High working range is another reason for using this type of actuators.

stewart2 Stewart

Design of 3-RRR Planar PM for Object Tracking

People Involved
   Mojtaba Yazdani

This manipulator contains three RRR limb actuated with three AX-23 Dynamixel motors fixed on the base. Similar to other manipulator designed in TaarLab, each R-joint includes four bearing to ensure the alignment and sufficient stiffness and all moving parts are made of AL 7075-T6 to minimize the moving inertia of the mechanism.
This mechanism could be used in object tracking application by installing a camera on its end-effector. By adding other parts to the specified places on its base, the manipulator could be used either in horizontal or vertical position.


Design, Model & Control of a 3 DOF PM for Humanoid Neck Motion Simulator

People Involved
 Behzad Danaei, Arvin Rasoulzadeh, Alaleh Arian

Human neck has a complex musculoskeletal structure with seven vertebrae and more than twenty muscles. One of the main functions of neck is controlling head movements. These movements are: head pan, head tilt and head swing. We are interested in simulating neck movements, via parallel manipulators. In this project we are hoping to achieve two main goals:

1. Designing, Modeling and Optimizing: First stage of the research is to design a manipulator which provides three rotational degree of freedom about a fixed point with acceptable workspace and stiffness and realistic motion speed. We use optimization methods mostly convex optimization to achieve these prospects.

2. Controlling and Human Interaction: As the second part of the project we are interested in controlling the robot with  brain signals extracted from an external headset, placed on users head. This part of the project involves fuzzy control and signal processing operations.

Results of this project can be used to help a person with neck movement problems, to control his/her head by just thinking about a desired movement!


Kinematic Optimization and Dimensional Synthesis of Parallel Robots

People Involved
   Amirhossein Karimi

Parallel robots play an important role in the industry nowadays, as witnessed by an increasing growth in a variety of their applications. However, the analyses of their kinematics, workspace, and singularities are of considerable complexity versus serial robots, as some of the problems in this field have been remained unsolved. Confrontation with singularities of parallel robots can be expressed in terms of three different approaches, namely: 1) synthesis considerations for designing mechanisms with fewer singularities 2) obtaining largest singularity-free zones within the workspace of the mechanisms to ensure the safety of these regions from singularity 3) to consider the singularity in the path generation procedure to obtain singularity-free paths. In this thesis, it is aimed at exerting analytical methods based on convex optimization to resolve problems caused by the singularities in the workspace of the mechanisms, including failure to implement control algorithms, collapse of mechanism configuration, and damage to the mechanical components of the robot.


Design, Development and Control of 3-RRR Planar Parallel Mechanism

People Involved
   Azadeh Droudchi, Mohammad Sharifzadeh, Mohsen Heydarzadeh

The 3-RRR Planar Parallel Mechanism is designed, constructed and controlled in Human and Robot Interaction Laboratory. The focus is on experimental control methods using inverse kinematic problem in order to gain more accuracy and smooth movement during the control process. Since there is no direct feedback sensor on the end-effector, all the foregoing control approaches could be regarded as open-loop control. In order to control the mechanism, two main control methods are used namely, position control and speed control. A Joy-stick is added to the system, in order to provide the ability for the user to control the mechanism directly. In addition, a Graphical User Interface is designed to help the user by three main control states. The first state is considered as off-line control, in which, the mechanism will follow a specific path defined in the program. In the second state, off-line control via Joy-stick, the mechanism will follow a path specified by the user via Joy-stick. As the third state, which is considered as the on-line control via Joy-stick, the mechanism will interactively follow a path specified by the user via the Joy-stick. All the programs are written in Qt creator in order to speed up data transmission from computer to the mechanism’s actuators and vice versa.

RRR picture low RRR assembly

Collision-Free Workspac of Parallel Robots based on Convex Optimization Approach

People Involved
Golnoush Asaeikheybari

Parallel robots play a vital role in today’s industry. The analysis of Kinematics, workspace and singularities of the proposed robots is of considerable complexity. The main contribution of this research is exerting analytical methods based on convex optimization to tackle the problems that arouse due to singularity. To reach this goal, the largest singularity free convex ellipsoid in the workspace of the proposed parallel robots will be extracted. To this purpose, new convex-optimization based algorithms will be introduced for 3-DOFs and 4-DOFs Delta and 3-UPU parallel robots. Mathematical knowledge in the fields of linear algebra and matrix analysis, convex optimization, algebraic geometry, and etc. is prerequisite for the analysis of the aforementioned purposes.




Agile Eye (2-DoF)

Agile Eye (2DoF)


Tripteron (3DoF)

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