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Figure 6-2: Default PD trajectory tracking performance.

Figure 6 -2: Default PD trajectory tracking performance.

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Figure 1-1: Common used industrial robotic systems. Taken from [6] [17]. irallel manipulators offer some advantages such as precision, mechanical stiffness and highe ad capacity, due to its parallel structure if compared with serial manipulators; on the other side disadvantage of parallel manipulators is the workspace limitations due to the link lengths anc e mechanical limits of the passive joints [30]. The most representative parallel manipulator i e Stewart-Gough platform. It consists of a fixed base and a mobile platform, connected by si: ismatic actuators or legs; this configuration provides six Degrees Of Freedom (DOF ), thre: anslational and three rotational, on its mobile platform. Parallel manipulators offer some advantages such as precision, mechanical stiffness and higher
Figure 1-1: Common used industrial robotic systems. Taken from [6] [17]. irallel manipulators offer some advantages such as precision, mechanical stiffness and highe ad capacity, due to its parallel structure if compared with serial manipulators; on the other side disadvantage of parallel manipulators is the workspace limitations due to the link lengths anc e mechanical limits of the passive joints [30]. The most representative parallel manipulator i e Stewart-Gough platform. It consists of a fixed base and a mobile platform, connected by si: ismatic actuators or legs; this configuration provides six Degrees Of Freedom (DOF ), thre: anslational and three rotational, on its mobile platform. Parallel manipulators offer some advantages such as precision, mechanical stiffness and higher
(b) Largest shake table in the world
(b) Largest shake table in the world
enerally, a Hexapod robot system consists of a Robot (mechanical structure), controller, Teacl endant, controller/computer, user documentation and accessories. These are the basic com onents that are generally included in any serious commercial robotic system. The “Hexapoc IDESI project" is divided at least in three phases, with the development of one prototyps ith increased capabilities in each phase; the current prototype (see Figure 1-3) correspond: ) the phase I, which is called “Hexapod CIDESI phase 1", better known by its nickname HxCf1" [29, 36]. In the Phase I, the robot is mainly intended as a low cost industrial-lik« xperimental prototype [21]. Figure 1-3: HxCfl Hexapod CIDESI project. Taken from [36].
enerally, a Hexapod robot system consists of a Robot (mechanical structure), controller, Teacl endant, controller/computer, user documentation and accessories. These are the basic com onents that are generally included in any serious commercial robotic system. The “Hexapoc IDESI project" is divided at least in three phases, with the development of one prototyps ith increased capabilities in each phase; the current prototype (see Figure 1-3) correspond: ) the phase I, which is called “Hexapod CIDESI phase 1", better known by its nickname HxCf1" [29, 36]. In the Phase I, the robot is mainly intended as a low cost industrial-lik« xperimental prototype [21]. Figure 1-3: HxCfl Hexapod CIDESI project. Taken from [36].
Figure 1-4: Occurrence of Earthquakes Globally (Digital Tectonic Activity Map (DTAM ), 2002). Taken from [4]. The seismicity or seismic activity of an area refers to the frequency, type and size of earthquakes experienced over a period of time. Earthquakes typically occur along tectonic plate boundaries, but some occur along fault lines in the middle of the plates as well. Countries around the Pacific Rim are heavily affected, as are many countries in the Mediterranean region and western and southern Asia(see Figure 1-4) [16].
Figure 1-4: Occurrence of Earthquakes Globally (Digital Tectonic Activity Map (DTAM ), 2002). Taken from [4]. The seismicity or seismic activity of an area refers to the frequency, type and size of earthquakes experienced over a period of time. Earthquakes typically occur along tectonic plate boundaries, but some occur along fault lines in the middle of the plates as well. Countries around the Pacific Rim are heavily affected, as are many countries in the Mediterranean region and western and southern Asia(see Figure 1-4) [16].
Figure 1-7: Estimated annual worldwide supply of industrial robots 2009-2017 and 2018*- 2021*. Taken from [5]
Figure 1-7: Estimated annual worldwide supply of industrial robots 2009-2017 and 2018*- 2021*. Taken from [5]
Figure 1-8: Estimated annual worldwide operational stock of industrial robots 2009-2017 and 2018*-2021*. Taken from [5]
Figure 1-8: Estimated annual worldwide operational stock of industrial robots 2009-2017 and 2018*-2021*. Taken from [5]
Figure 2-1: Stewart-Gough platform. Taken from [37]. Parallel kinematics precision positioning systems have many advantages over serial kinematics
Figure 2-1: Stewart-Gough platform. Taken from [37]. Parallel kinematics precision positioning systems have many advantages over serial kinematics
Figure 2-2: Geometrical configurations for Stewart-Gough platforms of 6 DOF. Taken from 2.1.2 Stewart-Gough platforms applications Stewart Gough platform was proposed originally as a mechanism for flight simulation but with
Figure 2-2: Geometrical configurations for Stewart-Gough platforms of 6 DOF. Taken from 2.1.2 Stewart-Gough platforms applications Stewart Gough platform was proposed originally as a mechanism for flight simulation but with
used to assure the performance. Design of the SP is showed in Figure 2-4.
used to assure the performance. Design of the SP is showed in Figure 2-4.
Figure 2-4: Proposed design structure of the fine tuning platform. Taken from [19].
Figure 2-4: Proposed design structure of the fine tuning platform. Taken from [19].
Figure 2-6: Hexapod configuration. Taken from [13] [27].
Figure 2-6: Hexapod configuration. Taken from [13] [27].
Table 3-1: Development phases for the CIDESI Hexapod project. Taken from [21] opment is divided in four phases, as shown in Table 3-1. The CIDESI Hexapod project aims is high and in order to achieve the desired result, its devel- The CIDESI Hexapod HxCf1 robotic system is a project that aims to develop an industrial grade robotic system that provides similar functionalities to the ones found in a common used indus- trial robot. The Hexapod robotic system project consists of the parallel robot, the controller, Human Machine Interface (HMI ), and a user documentation; all these as the basic components that are generally included in a commercial robotic system used in the industry.
Table 3-1: Development phases for the CIDESI Hexapod project. Taken from [21] opment is divided in four phases, as shown in Table 3-1. The CIDESI Hexapod project aims is high and in order to achieve the desired result, its devel- The CIDESI Hexapod HxCf1 robotic system is a project that aims to develop an industrial grade robotic system that provides similar functionalities to the ones found in a common used indus- trial robot. The Hexapod robotic system project consists of the parallel robot, the controller, Human Machine Interface (HMI ), and a user documentation; all these as the basic components that are generally included in a commercial robotic system used in the industry.
First, the parts that form the universal joints were assembled and fixed robot. Then, the linear actuators were assembled with the universal j adding the head couplings on the top of the shaft of the actuators. Af to the base platform of the oints and secured in place er this, the spherical joints were screwed in the mobile platform,secured with bolts and the coupling disc was assemblec to the mobile platform. Finally, all the actuators were assembled o the spherical joints anc secured in place with screws. The assembled robot highlighting the main components is showr in Figure 3-1 [21]. Figure 3-1: Assembled CIDESI Hexapod system. Taken from [21]. secured in place with screws. The assembled robot highlighting the main components is shown
First, the parts that form the universal joints were assembled and fixed robot. Then, the linear actuators were assembled with the universal j adding the head couplings on the top of the shaft of the actuators. Af to the base platform of the oints and secured in place er this, the spherical joints were screwed in the mobile platform,secured with bolts and the coupling disc was assemblec to the mobile platform. Finally, all the actuators were assembled o the spherical joints anc secured in place with screws. The assembled robot highlighting the main components is showr in Figure 3-1 [21]. Figure 3-1: Assembled CIDESI Hexapod system. Taken from [21]. secured in place with screws. The assembled robot highlighting the main components is shown
jrk drivers, and the AND gate circuit, three protoboards were used (see Figure 3-2). The base of the prototype is a plastic plate where all components are fixed. This material was used because unlike wood, acrylic, or metal, it is easy and fast to make fixation points for the components. For the connection of the power supply channels, the communication lines of the jrk drivers, and the AND gate circuit, three protoboards were used (see Figure 3-2).
jrk drivers, and the AND gate circuit, three protoboards were used (see Figure 3-2). The base of the prototype is a plastic plate where all components are fixed. This material was used because unlike wood, acrylic, or metal, it is easy and fast to make fixation points for the components. For the connection of the power supply channels, the communication lines of the jrk drivers, and the AND gate circuit, three protoboards were used (see Figure 3-2).
Figure 3-3: Robot electrical connections. Taken from [21]. 3.2.8.2 Software The software part of the controller was implemented as modules; these modules were imple- mented as C++ classes, whose internal parameters can be read from a configuration file and initialized inside a class constructor. Communication between classes is achieved by allowing class methods to call other methods from other classes [21]. The software part of the controller was implemented as modules; these modules were imple-
Figure 3-3: Robot electrical connections. Taken from [21]. 3.2.8.2 Software The software part of the controller was implemented as modules; these modules were imple- mented as C++ classes, whose internal parameters can be read from a configuration file and initialized inside a class constructor. Communication between classes is achieved by allowing class methods to call other methods from other classes [21]. The software part of the controller was implemented as modules; these modules were imple-
4.1.1 Base and Mobile platforms configuration
4.1.1 Base and Mobile platforms configuration
Figure 4-2: Angle characterization for the mobile platform using its coordinate system Tyy,. —aeO: nr ass. aie The Figure 4-2 is a schematic representation of the mobile platform, where the coordinate system
Figure 4-2: Angle characterization for the mobile platform using its coordinate system Tyy,. —aeO: nr ass. aie The Figure 4-2 is a schematic representation of the mobile platform, where the coordinate system
actuator and values for A; to A¢ is obtained using 6, as a known value. The Figure 4-3 show the characterization of points G7;, where i represent the number of each The Figure 4-4 is a schematic representation of the base platform, where the coordinate syster
actuator and values for A; to A¢ is obtained using 6, as a known value. The Figure 4-3 show the characterization of points G7;, where i represent the number of each The Figure 4-4 is a schematic representation of the base platform, where the coordinate syster
The parameters to take into account in order to define the Hexapod base and mobile platform
The parameters to take into account in order to define the Hexapod base and mobile platform
(b) Schematic representation for v2, v4 and v6. Figure 4-5: Schematic representation of the base platform. Taken from [13]. actuator and values for v; to v6 is obtained using @, as a known value.
(b) Schematic representation for v2, v4 and v6. Figure 4-5: Schematic representation of the base platform. Taken from [13]. actuator and values for v; to v6 is obtained using @, as a known value.
Table 4-2: Point coordinates for B; and GT;. Taken from [13]
Table 4-2: Point coordinates for B; and GT;. Taken from [13]
Where G7; is the position vector from the union points of the mobile platform with each one of the six actuators taking as base the coordinate system 7} using the trigonometric functions that apply for each actuator depending if it is even or odd. For the base platform the same procedure is done, just adjusting the value of the corresponding parameters as it was mentioned in Figure 4-2, Figure 4-3 and Table 4-2.
Where G7; is the position vector from the union points of the mobile platform with each one of the six actuators taking as base the coordinate system 7} using the trigonometric functions that apply for each actuator depending if it is even or odd. For the base platform the same procedure is done, just adjusting the value of the corresponding parameters as it was mentioned in Figure 4-2, Figure 4-3 and Table 4-2.
Using this calculations as base, it is possible to determine if the actuators are able to move from one point to another at the desired speed. If one movement require a speed higher than the maximum speed given by the actuators of the prototype (14.6 mm/s), the movement or routine cannot be reproduced by the SP.
Using this calculations as base, it is possible to determine if the actuators are able to move from one point to another at the desired speed. If one movement require a speed higher than the maximum speed given by the actuators of the prototype (14.6 mm/s), the movement or routine cannot be reproduced by the SP.
the following equation for velocity is defined:
the following equation for velocity is defined:
sition sensor of the mobile platform, 7.Mobile platform position error, 8.Leg position position
sition sensor of the mobile platform, 7.Mobile platform position error, 8.Leg position position
Figure 5-2: CIDESI HxCf1 Hexapod exported geometry.
Figure 5-2: CIDESI HxCf1 Hexapod exported geometry.
Figure 5-3: CIDESI HxCf1 Hexapod visual output.
Figure 5-3: CIDESI HxCf1 Hexapod visual output.
For this tests, unscaled records are going to be used, having a search engine with several options in order to be more specific about the record that the user is looking for. The PG@MD SEARCH ENGINE window for the unscaled section contains nine main parts, as labeled in Figure 5-4: (1) Main Search Engine; (2) Supplementary Search Engine to specify the record acceptance cri- teria and perform search over PEER database; (3) Spectra plotting window; (4) Ground motion record information output list; (5) Google map to display geographic location as well as basic information about each record checked; (6) Acceleration/ Velocity/ Displacement time series plotting of a selected record; (7) Zoom In time function for examining the time series of an individual record; (8) Graphic control panel for line styles and maximum number of output to be listed; (9) Buttons to save the search results and selected acceleration time series files. be listed; (9) Buttons to save the search results and selected acceleration time series files.
For this tests, unscaled records are going to be used, having a search engine with several options in order to be more specific about the record that the user is looking for. The PG@MD SEARCH ENGINE window for the unscaled section contains nine main parts, as labeled in Figure 5-4: (1) Main Search Engine; (2) Supplementary Search Engine to specify the record acceptance cri- teria and perform search over PEER database; (3) Spectra plotting window; (4) Ground motion record information output list; (5) Google map to display geographic location as well as basic information about each record checked; (6) Acceleration/ Velocity/ Displacement time series plotting of a selected record; (7) Zoom In time function for examining the time series of an individual record; (8) Graphic control panel for line styles and maximum number of output to be listed; (9) Buttons to save the search results and selected acceleration time series files. be listed; (9) Buttons to save the search results and selected acceleration time series files.
acceleration are displayed in Figure 5-5. In order to perform simulations with the linear actuators, glideforce LACT6P, an earthquake record with displacements in the order of millimetres was chosen. The record number of the selected earthquake is 10058 and the name of the same is Sparks, recorded in the Oklahoma station in the USA; the full information of the mentioned record as well as the peak spectra acceleration are displayed in Figure 5-5. station in the USA; the full information of the mentioned record as well as the peak spectra
acceleration are displayed in Figure 5-5. In order to perform simulations with the linear actuators, glideforce LACT6P, an earthquake record with displacements in the order of millimetres was chosen. The record number of the selected earthquake is 10058 and the name of the same is Sparks, recorded in the Oklahoma station in the USA; the full information of the mentioned record as well as the peak spectra acceleration are displayed in Figure 5-5. station in the USA; the full information of the mentioned record as well as the peak spectra
Table 5-1: Linear actuator parameters. Taken from [2] inear friction and the screw drive efficiency; parameters are shown in Table 5-1.
Table 5-1: Linear actuator parameters. Taken from [2] inear friction and the screw drive efficiency; parameters are shown in Table 5-1.
Figure 5-6: Earthquake components time series for acceleration, velocity and position.
Figure 5-6: Earthquake components time series for acceleration, velocity and position.
In order to test the Direct current (DC ) motor model, the two equilibrium conditions were tested, the first one with no external load (0 N), and the second one with full load capacity (500 N); after performing the simulation, the linear velocity was plotted in order to see if the maximum velocity in each condition corresponds to the one defined in the actuator data sheet [2] by the fabricator. The resulting plots shown in Figure 5-8 show that the velocity in each condition corresponds to the given ones by the fabricator (see Figure 5-9).
In order to test the Direct current (DC ) motor model, the two equilibrium conditions were tested, the first one with no external load (0 N), and the second one with full load capacity (500 N); after performing the simulation, the linear velocity was plotted in order to see if the maximum velocity in each condition corresponds to the one defined in the actuator data sheet [2] by the fabricator. The resulting plots shown in Figure 5-8 show that the velocity in each condition corresponds to the given ones by the fabricator (see Figure 5-9).
Figure 5-8: Simscape DC motor model simulation. corresponds to the given ones by the fabricator (see Figure 5-9).
Figure 5-8: Simscape DC motor model simulation. corresponds to the given ones by the fabricator (see Figure 5-9).
Figure 6-1: Closed loop DC motor model.
Figure 6-1: Closed loop DC motor model.
6.2 Ziegler Nichols tuning The Ziegler-Nichols method allows to adjust or "tune" a PID controller empirically, without knowing the plant or the controlled system equations. These adjustment rules proposed by Ziegler and Nichols [41] were published in 1942 and since then it is one of the most widely used and widely used tuning methods. The values proposed by this method try to achieve in the feedback system a step response with a maximum overshoot of 25%, which is a robust value with good characteristics of speed and stability for most systems. Ziegler and Nichols [41] were published in 1942 and since then it is one of the most widely
6.2 Ziegler Nichols tuning The Ziegler-Nichols method allows to adjust or "tune" a PID controller empirically, without knowing the plant or the controlled system equations. These adjustment rules proposed by Ziegler and Nichols [41] were published in 1942 and since then it is one of the most widely used and widely used tuning methods. The values proposed by this method try to achieve in the feedback system a step response with a maximum overshoot of 25%, which is a robust value with good characteristics of speed and stability for most systems. Ziegler and Nichols [41] were published in 1942 and since then it is one of the most widely
method was discarded and other one was proposed in order to improve the performance of th The main goal of the PID controller is to improve the performance of the system, and the default The main goal of the PID controller is to improve the performance of the system, and the default configuration is normally not the optimal in order to obtain the desired results. Based on the bode plots of the proposed DC motor model, because Equation 6.1 is the PID controller in order to define the values for K,, K; and Kp. Using this gains will allow the system to improve disturbance rejection, add phase lead, improve phase margin,and speeding up the response. disturbance rejection, add phase lead, improve phase margin,and speeding up the response.
method was discarded and other one was proposed in order to improve the performance of th The main goal of the PID controller is to improve the performance of the system, and the default The main goal of the PID controller is to improve the performance of the system, and the default configuration is normally not the optimal in order to obtain the desired results. Based on the bode plots of the proposed DC motor model, because Equation 6.1 is the PID controller in order to define the values for K,, K; and Kp. Using this gains will allow the system to improve disturbance rejection, add phase lead, improve phase margin,and speeding up the response. disturbance rejection, add phase lead, improve phase margin,and speeding up the response.
Figure 6-5: Tuned PID trajectory tracking performance. frequency in the system characterization. the phase margin. In Figure 6-5 the trajectory tracking performance of the controller (control voltage and position error) is shown, having a mean square error of MSE=0.0180, improving the previous performance with the default PD; also we can observe in Figure 6-6 the bode plot of this configuration, having the crossover frequency in 15rad/s, pretty close to the calculated frequency in the system characterization. of this configuration, having the crossover frequency in 15rad/s, pretty close to the calculated
Figure 6-5: Tuned PID trajectory tracking performance. frequency in the system characterization. the phase margin. In Figure 6-5 the trajectory tracking performance of the controller (control voltage and position error) is shown, having a mean square error of MSE=0.0180, improving the previous performance with the default PD; also we can observe in Figure 6-6 the bode plot of this configuration, having the crossover frequency in 15rad/s, pretty close to the calculated frequency in the system characterization. of this configuration, having the crossover frequency in 15rad/s, pretty close to the calculated
Figure 7-1: PD desired against real actuator Length. Table 7-1: PD MSE of actuators and mobile platform.
Figure 7-1: PD desired against real actuator Length. Table 7-1: PD MSE of actuators and mobile platform.
Figure 7-2: PD leg length error.
Figure 7-2: PD leg length error.
and for the mobile platform coordinate system are summarized in Table 7-2.
and for the mobile platform coordinate system are summarized in Table 7-2.
Figure 7-6: PID desired against real actuator Length.
Figure 7-6: PID desired against real actuator Length.
Figure 7-8: PID mobile platform axis position.
Figure 7-8: PID mobile platform axis position.
Table 8-1: PD MSE of actuators 1, 3 and 5.
Table 8-1: PD MSE of actuators 1, 3 and 5.
Figure 8-1: Default PD actuator measured positions against desired positions.
Figure 8-1: Default PD actuator measured positions against desired positions.
Figure 8-5: Proposed PD measured positions against desired positions.
Figure 8-5: Proposed PD measured positions against desired positions.
Figure 8-7: Proposed PD actuator 1, 3 and 5 experimental control voltage.
Figure 8-7: Proposed PD actuator 1, 3 and 5 experimental control voltage.
Figure A-1: Chronogram.
Figure A-1: Chronogram.
Dimensions — Actuator With Potentiometer
Dimensions — Actuator With Potentiometer
Note: Above graphs and performance data do not apply to the “Q” (quiet) option.
Note: Above graphs and performance data do not apply to the “Q” (quiet) option.
Related topics:
GeologyPid ControllerStewart platformPARALLEL MANIPULATOR
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