Optimal Trajectory Generation of Parallel Manipulator

*Chandan Choubey and Jyoti Ohri*

## **Abstract**

In this paper we have designed an optimal trajectory generation (OTG) method to generate easy and errortless continuous path motion with quick converging by using Gray Wolf Optimization (GWO) method. This OTG method finds the trajectory path with minimum tracking-error, combined speed, joint increasing speed wrinkle as well as joint lurching move to follow a smooth along with error-free continuous path.

**Keywords:** Gray Wolf Optimization, Trajectory Generation algorithm, Parallel Manipulators, Error-Free Path Motion

#### **1. Introduction**

We know that the biological system basically influence the field of robot like the upper portion of human arm with a few sequential connections, this serial structure are called serial robots. The serial robots structure acquire large space, lack of precision and low load handling capability are its major drawbacks. Parallel manipulators was introduced by the researchers to reduce the disadvantages of series manipulators [1, 2].

The performance of parallel manipulator has become more advance in the recent scenario as compared to the series manipulator. The parallel manipulator has so many benefits as compared to series like precision, load handling ability, accuracy and many more. The parallel manipulators are used in aerodynamics [3], medical surgery [4–7], machine equipment's [8, 9], and object pick and place [10, 11].

A parallel manipulator consist of a movable plate connected with a fixed plate with hinged legs which is controlled by a dc motor separately. The number of orientation of legs is considered as degrees of freedom (DOF) of movable plate with respect to fixed plate, this type of arrangement is called as coupling systems.

The parallel robotic arm generally provides high and smooth speed, acceleration with accurate path tracking. For tracking continuous path, parallel manipulator must satisfied following specifications like error-free tracking, minimum settling time and robustness against uncertainties [12].

#### **2. Literature survey**

Almas shintemirov *et.al* [13] proposed an optimal path by spherical parallel manipulator (SPM), controlled by servomotors with default setting of position control. For such type of system there are three approaches to get forward kinematics, a structural space and servomotors reference paths.

Damien six *et.al* [14] had evolved a new flying robot considered as one of parallel manipulators. This robot has three similar legs connected between fixed and moving stages, are controlled by quadrotors a stage. For constructing new architecture of aerial robotics, requires quadrotor with strong body.

parts as well as in end-machining of middle tolerance parts, have increased their

An input is produced in the control system of the robotic manipulators by trajectory generation for executing the required task with satisfactory performance since a path-constrained motion is followed by the robotic manipulator. The path of the robotic trajectories is assembled offline at first, and later it is assembled online by the end-effectors. There are two approaches in offline trajectory - hand level and

By using opposite kinematics, the Cartesian coordinates are transformed into joint coordinates. Joint level approach costs less expensive in terms of computational complexity than other approaches while controlling the robotic manipulators. Moreover, this joint level approach has an added advantage of considering only the kinematic constraints during the trajectory generation, while ignoring the dynamic

An Optimal Trajectory Generation Algorithm (OTGA) [20] is developed to generate smooth motion trajectories with minimum time for Dof parallel manipulators. For optimal trajectory generation, the Gray Wolf technique is employed with constraints and objective functions, this proposed OTG algorithm uses minimal tracking error. Moreover, for smooth continuous motion of the robotic manipulators, joint speed, acceleration and jerks were also considered along with it. So by using both objective constraints, the Gray Wolf optimization technique selects an

A reference trajectory is created by using the developed Optimal Trajectory Generation [21] manipulators. The path constraint motion of the industrial robots plays a vital role in welding, cutting, surgery and machining applications. A sample

joint level. By using Jacobian transformation, these joint coordinates are

transformed into Cartesian coordinates for each sampling.

optimal trajectory at every iteration as shown in **Figure 1**.

reference trajectory with 15 segments is shown below in **Figure 2**.

**3.1 Trajectory generation remarks**

**Figure 1.**

**61**

*The schematic diagram of OTGA.*

constraints that increase the computational effort.

*Optimal Trajectory Generation of Parallel Manipulator DOI: http://dx.doi.org/10.5772/intechopen.96462*

usage rapidly.

Soheil zarkandi [15] had proposed a parallel manipulator for CNC machine, used for object holding in the 4-axis. This manipulator has two degree-of-freedom i.e. translational and rotational. It consist of two translational DOF and one rotational DOF.

Guilherme sartori Natal *et.al* [16] had tentatively compared the R4 controlled type manipulator with three control methods and provides high acceleration. First method, the redundant controlling is specifically done by a PID controller in working space. Secondly, based on dynamic configuration of redundant R4, a dual working space with feed forward control method was implemented because of impropriate outcomes of first method. Thirdly, upgrading such type of controller, generates high acceleration above 100G in order to achieve path tracking.

Bikash kumar Sarkar [17], had shown the reproduction concentrate over the using pressurized water activated 2DOF equal controller pondered to the posture (hurl and pitch) control application. The framework model is pondered to the ease pressure driven part setups like corresponding valve with dead band, low speed water powered chamber and so forth. The streamlined numerical model of the controller has been created in this investigation. To examine the control execution by a model free fluffy tuned feed forward inclination PID regulator for present control application, this model has been utilized.

Yogesh singh *et.al* [18] has introduced a controller called U-formed planar equal controller which tends to the opposite elements of three levels of opportunity (DOF) where the introduced controller has three legs comprising of kaleidoscopic revolute (PPR) joint course of action in which every leg had one dynamic kaleidoscopic joint. A versatile sliding mode control, joined with an aggravation onlooker for the movement control of the controller was evaluated like a relative subsidiary (PD). The controlled mechanical controller was changed into decoupled elements utilizing this plan thus that the movement execution was gainful to quantify.

Jiantao Yao *et.al* [19] has built up the ability and the exhibition of the equal controller as for the repetitive incitation. While expanding a drive for the center PRPU uninvolved imperative branch to make it an excess incitation branch, it is expected to manage coordination and circulation of the main impetus of the equal controller with repetitive activation and need to understand the control system dependent on elements, based on the first 5UPS/PRPU equal controller. The component that exist the repetitive incitation from the viewpoint of level of opportunity and settled in a powerful model dependent on Lagrangian technique is improved by bringing in the arrangements excess sorts and pieces of 5UPS/PRPU equal controller with repetitive activation.

### **3. Optimal trajectory generation algorithm**

The industrial robots were broadly used in various fields like automotive and aircraft industries and many more. The use of industrial robots, generally carry out repeated tasks such as pick and place, welding, assembling, etc. Their adaptability and capability to perform complex tasks in a significant workspace makes them useful in SME (small and medium enterprise). The characteristic advantages they offer in machine applications like prototyping, cleaning and pre-machining of cast

### *Optimal Trajectory Generation of Parallel Manipulator DOI: http://dx.doi.org/10.5772/intechopen.96462*

control. For such type of system there are three approaches to get forward

moving stages, are controlled by quadrotors a stage. For constructing new architecture of aerial robotics, requires quadrotor with strong body.

generates high acceleration above 100G in order to achieve path tracking.

control application, this model has been utilized.

**3. Optimal trajectory generation algorithm**

with repetitive activation.

**60**

Damien six *et.al* [14] had evolved a new flying robot considered as one of parallel manipulators. This robot has three similar legs connected between fixed and

Soheil zarkandi [15] had proposed a parallel manipulator for CNC machine, used for object holding in the 4-axis. This manipulator has two degree-of-freedom i.e. translational and rotational. It consist of two translational DOF and one rotational

Guilherme sartori Natal *et.al* [16] had tentatively compared the R4 controlled type manipulator with three control methods and provides high acceleration. First method, the redundant controlling is specifically done by a PID controller in working space. Secondly, based on dynamic configuration of redundant R4, a dual working space with feed forward control method was implemented because of impropriate outcomes of first method. Thirdly, upgrading such type of controller,

Bikash kumar Sarkar [17], had shown the reproduction concentrate over the using pressurized water activated 2DOF equal controller pondered to the posture (hurl and pitch) control application. The framework model is pondered to the ease pressure driven part setups like corresponding valve with dead band, low speed water powered chamber and so forth. The streamlined numerical model of the controller has been created in this investigation. To examine the control execution by a model free fluffy tuned feed forward inclination PID regulator for present

Yogesh singh *et.al* [18] has introduced a controller called U-formed planar equal

The industrial robots were broadly used in various fields like automotive and aircraft industries and many more. The use of industrial robots, generally carry out repeated tasks such as pick and place, welding, assembling, etc. Their adaptability and capability to perform complex tasks in a significant workspace makes them useful in SME (small and medium enterprise). The characteristic advantages they offer in machine applications like prototyping, cleaning and pre-machining of cast

controller which tends to the opposite elements of three levels of opportunity (DOF) where the introduced controller has three legs comprising of kaleidoscopic revolute (PPR) joint course of action in which every leg had one dynamic kaleidoscopic joint. A versatile sliding mode control, joined with an aggravation onlooker for the movement control of the controller was evaluated like a relative subsidiary (PD). The controlled mechanical controller was changed into decoupled elements utilizing this plan thus that the movement execution was gainful to quantify. Jiantao Yao *et.al* [19] has built up the ability and the exhibition of the equal controller as for the repetitive incitation. While expanding a drive for the center PRPU uninvolved imperative branch to make it an excess incitation branch, it is expected to manage coordination and circulation of the main impetus of the equal controller with repetitive activation and need to understand the control system dependent on elements, based on the first 5UPS/PRPU equal controller. The component that exist the repetitive incitation from the viewpoint of level of opportunity and settled in a powerful model dependent on Lagrangian technique is improved by bringing in the arrangements excess sorts and pieces of 5UPS/PRPU equal controller

kinematics, a structural space and servomotors reference paths.

*Collaborative and Humanoid Robots*

DOF.

parts as well as in end-machining of middle tolerance parts, have increased their usage rapidly.

An input is produced in the control system of the robotic manipulators by trajectory generation for executing the required task with satisfactory performance since a path-constrained motion is followed by the robotic manipulator. The path of the robotic trajectories is assembled offline at first, and later it is assembled online by the end-effectors. There are two approaches in offline trajectory - hand level and joint level. By using Jacobian transformation, these joint coordinates are transformed into Cartesian coordinates for each sampling.

By using opposite kinematics, the Cartesian coordinates are transformed into joint coordinates. Joint level approach costs less expensive in terms of computational complexity than other approaches while controlling the robotic manipulators. Moreover, this joint level approach has an added advantage of considering only the kinematic constraints during the trajectory generation, while ignoring the dynamic constraints that increase the computational effort.

An Optimal Trajectory Generation Algorithm (OTGA) [20] is developed to generate smooth motion trajectories with minimum time for Dof parallel manipulators. For optimal trajectory generation, the Gray Wolf technique is employed with constraints and objective functions, this proposed OTG algorithm uses minimal tracking error. Moreover, for smooth continuous motion of the robotic manipulators, joint speed, acceleration and jerks were also considered along with it. So by using both objective constraints, the Gray Wolf optimization technique selects an optimal trajectory at every iteration as shown in **Figure 1**.
