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™”rJ+ïsN@ÂD„>rÝ1÷2Za’Ý÷¼Œ†ôù‡9(Çæ$ì56üºe"çd4„Zô(çe4dÖÎÁe4ÐרB“—Ñ0aštA'£!ôæºÇád4ì{–Ñhèe´‚�ÔË0îd´âÑ/£ÝÈw1B5Ðh á¤HyÌÑh¨'ÝMq 4
|
YÓUc£Ž†Í…çðÒëh@cžng¯£ñ¡¦)E
|
||||||
UÍ�†¤¶>˜,o£a¢Ðlõ l´Žy·…¹íÁõpƒ¼�ö|Õ}ØÁFêÿÂÂlK4öš. 4 4Ú3#å�FCýG·l\o£�E*£™ÑãhÀ
|
|
||||||
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|
ùÕ�Ãäu4dlàNl–Ù¨£¢Ù»‰ît´�¿¯Sw䜎†!ô™Šz
|
||||||
qÙFëu48Y›^§QGCf_íN·×Ñ0,Ÿ�–çx4dpÓ_ª4HàÑê˜ëx4ºÊ©£¼OÇ£!Aé2£)ðhX1ö À£aMàÈ%ñhر¸9(aI<–曥ë �†Ç½»î�GÃðXì "ðhHÞïdJàÑÐqX9tI<Ž éì™Gs¼tàÑ®‡�H<7g!q@ s>ÒÏïSŸÑéhíK{�äM:
|
qÙFëu48Y›^§QGCf_íN·×Ñ0,Ÿ�–çx4dpÓ_ª4HàÑê˜ëx4ºÊ©£¼OÇ£!Aé2£)ðhX1ö À£aMàÈ%ñhر¸9(aI<–曥ë �†Ç½»î�GÃðXì "ðhHÞïdJàÑÐqX9tI<Ž éì™Gs¼tàÑ®‡�H<7g!q@ s>ÒÏïSŸÑéhíK{�äM:
|
||||||
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|
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|
||||||
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|
šêhÎ¥×Ñ*ïûwÃmL=B#�HȈZ"ŽÆžÝ(d2ãq4”³–ž€çq4ìÏ!±GBé<ŽÆú=Ðãh˜ÐOVÏg=Ž†²xú^õ®îq4®a§ ´È;GÃñü-ca´ÑP8Î(ˆX1ÞFC ø½ ¢j �§xE9‚€£q ãjŸ¦ÃÑpÂCœ<4âh�ò¼ÂXŽ†(ò�ׇKÂÑø,XÏ ‚�†âãµj$U°Ñ°1.YÄK²ÑŽÑ 6ÚÉ�(ë�FãªSe�† ôS*ˆŒFCCígvF»0
|
||||||
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|
8Lòñ0§�6ÞãM0¶*ªEná²¹m€Ñ°ö= 50¶8nÛW 0Ö°�yça´û¹3F�w5QÍ»h¨¹h½ÀÄËh¨–.½JÓËhлhdÅaÁe4Ôjðò?Ãh(¶Ün‹{õ0§Â]›@ÎE;ØÞ³fêà¢mp•ì\$¸ht!Ò/N£Yƒ‹¶#°ë**\´ u ô¦å+ð2ZÅ �‹÷—$£U þd´ú%µ:2
|
||||||
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|
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|
||||||
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|
Ë™µ4ÙT 2Âé¸ Kè0'£�c9l�Ñ^Á'âòœNFC):ón¢Ÿ9
|
||||||
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|
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|
||||||
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|
mØr‘-IFk 96Íã 2ŽC#I‚Œ†½á£é騧Ñнxò0¶�+_zW´§Ñ°Í.Á¢‡9`Ÿâ:¤V,Øh(Îm›êÞÁFÛœdèm4gü}ñ7äm4Lñ¼ó0¤S.ò’Ç Œ†!“IyÌÁh'÷áéYy ÑPcÓ3j�Æá"§žÓ
|
||||||
h»N‰� 4Úùu‰)&þ˜£Ñ�±A£¶4�íBÑ!7z,ÑFCmƵ
|
h»N‰� 4Úùu‰)&þ˜£Ñ�±A£¶4�íBÑ!7z,ÑFCmƵ
|
||||||
|
|||||||
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<title>Study of the Flexible Joints</title>
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<title>Study of the Flexible Joints</title>
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<ul>
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<ul>
|
||||||
<li><a href="#orge032d30">1. Bending and Torsional Stiffness</a>
|
<li><a href="#orge032d30">1. Bending and Torsional Stiffness</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org4af6fbb">1.1. Initialization</a></li>
|
<li><a href="#org14d57c4">1.1. Initialization</a></li>
|
||||||
<li><a href="#orgde60939">1.2. Realistic Bending Stiffness Values</a>
|
<li><a href="#orgde60939">1.2. Realistic Bending Stiffness Values</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org1f64e69">1.2.1. Direct Velocity Feedback</a></li>
|
<li><a href="#org5ed48b8">1.2.1. Direct Velocity Feedback</a></li>
|
||||||
<li><a href="#org7eb4054">1.2.2. Primary Plant</a></li>
|
<li><a href="#orgddae25e">1.2.2. Primary Plant</a></li>
|
||||||
<li><a href="#org81a1a77">1.2.3. Conclusion</a></li>
|
<li><a href="#orgb8a9692">1.2.3. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org8ad3f34">1.3. Parametric Study</a>
|
<li><a href="#org8ad3f34">1.3. Parametric Study</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org1575b3d">1.3.1. Direct Velocity Feedback</a></li>
|
<li><a href="#org44ccdbe">1.3.1. Direct Velocity Feedback</a></li>
|
||||||
<li><a href="#orgb35fa00">1.3.2. Primary Control</a></li>
|
<li><a href="#org5d9965b">1.3.2. Primary Control</a></li>
|
||||||
<li><a href="#org4a1264f">1.3.3. Conclusion</a></li>
|
<li><a href="#org0f9f990">1.3.3. Conclusion</a></li>
|
||||||
</ul>
|
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|
||||||
</li>
|
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|
||||||
</ul>
|
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|
||||||
@@ -58,22 +58,22 @@
|
|||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org969d9e7">2.1. Realistic Translation Stiffness Values</a>
|
<li><a href="#org969d9e7">2.1. Realistic Translation Stiffness Values</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org14d57c4">2.1.1. Initialization</a></li>
|
<li><a href="#org8fdef7f">2.1.1. Initialization</a></li>
|
||||||
<li><a href="#org790d5e4">2.1.2. Direct Velocity Feedback</a></li>
|
<li><a href="#orgc087bb9">2.1.2. Direct Velocity Feedback</a></li>
|
||||||
<li><a href="#orgddae25e">2.1.3. Primary Plant</a></li>
|
<li><a href="#org4069e58">2.1.3. Primary Plant</a></li>
|
||||||
<li><a href="#org7ebf071">2.1.4. Conclusion</a></li>
|
<li><a href="#org3d8a1a7">2.1.4. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org0275632">2.2. Parametric study</a>
|
<li><a href="#org0275632">2.2. Parametric study</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org5ed48b8">2.2.1. Direct Velocity Feedback</a></li>
|
<li><a href="#orgdb214f9">2.2.1. Direct Velocity Feedback</a></li>
|
||||||
<li><a href="#org5d9965b">2.2.2. Primary Control</a></li>
|
<li><a href="#org53e5f08">2.2.2. Primary Control</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org8ee81cd">2.3. Conclusion</a></li>
|
<li><a href="#org1ddd8bf">2.3. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#orgb8a9692">3. Conclusion</a></li>
|
<li><a href="#orga32adf0">3. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@@ -106,8 +106,8 @@ In this section, we wish to study the effect of the rotation flexibility of the
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org4af6fbb" class="outline-3">
|
<div id="outline-container-org14d57c4" class="outline-3">
|
||||||
<h3 id="org4af6fbb"><span class="section-number-3">1.1</span> Initialization</h3>
|
<h3 id="org14d57c4"><span class="section-number-3">1.1</span> Initialization</h3>
|
||||||
<div class="outline-text-3" id="text-1-1">
|
<div class="outline-text-3" id="text-1-1">
|
||||||
<p>
|
<p>
|
||||||
Let’s initialize all the stages with default parameters.
|
Let’s initialize all the stages with default parameters.
|
||||||
@@ -168,8 +168,8 @@ This corresponds to the optimal identified stiffness.
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org1f64e69" class="outline-4">
|
<div id="outline-container-org5ed48b8" class="outline-4">
|
||||||
<h4 id="org1f64e69"><span class="section-number-4">1.2.1</span> Direct Velocity Feedback</h4>
|
<h4 id="org5ed48b8"><span class="section-number-4">1.2.1</span> Direct Velocity Feedback</h4>
|
||||||
<div class="outline-text-4" id="text-1-2-1">
|
<div class="outline-text-4" id="text-1-2-1">
|
||||||
<p>
|
<p>
|
||||||
We identify the dynamics from actuators force \(\tau_i\) to relative motion sensors \(d\mathcal{L}_i\) with and without considering the flexible joint stiffness.
|
We identify the dynamics from actuators force \(\tau_i\) to relative motion sensors \(d\mathcal{L}_i\) with and without considering the flexible joint stiffness.
|
||||||
@@ -189,8 +189,8 @@ It is shown that the adding of stiffness for the flexible joints does increase a
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org7eb4054" class="outline-4">
|
<div id="outline-container-orgddae25e" class="outline-4">
|
||||||
<h4 id="org7eb4054"><span class="section-number-4">1.2.2</span> Primary Plant</h4>
|
<h4 id="orgddae25e"><span class="section-number-4">1.2.2</span> Primary Plant</h4>
|
||||||
<div class="outline-text-4" id="text-1-2-2">
|
<div class="outline-text-4" id="text-1-2-2">
|
||||||
<p>
|
<p>
|
||||||
Let’s now identify the dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs).
|
Let’s now identify the dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs).
|
||||||
@@ -205,13 +205,13 @@ The plant dynamics is not found to be changing significantly.
|
|||||||
<div id="org4322feb" class="figure">
|
<div id="org4322feb" class="figure">
|
||||||
<p><img src="figs/flex_joints_rot_primary_plant_L.png" alt="flex_joints_rot_primary_plant_L.png" />
|
<p><img src="figs/flex_joints_rot_primary_plant_L.png" alt="flex_joints_rot_primary_plant_L.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 2: </span>Dynamics from \(\bm{\tau}^\prime_i\) to \(\bm{\epsilon}_{\mathcal{X}_n,i}\) with perfect joints (dashed) and with flexible joints (solid)</p>
|
<p><span class="figure-number">Figure 2: </span>Dynamics from \(\bm{\tau}^\prime_i\) to \(\bm{\epsilon}_{\mathcal{X}_n,i}\) with perfect joints and with flexible joints</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org81a1a77" class="outline-4">
|
<div id="outline-container-orgb8a9692" class="outline-4">
|
||||||
<h4 id="org81a1a77"><span class="section-number-4">1.2.3</span> Conclusion</h4>
|
<h4 id="orgb8a9692"><span class="section-number-4">1.2.3</span> Conclusion</h4>
|
||||||
<div class="outline-text-4" id="text-1-2-3">
|
<div class="outline-text-4" id="text-1-2-3">
|
||||||
<div class="important">
|
<div class="important">
|
||||||
<p>
|
<p>
|
||||||
@@ -248,8 +248,8 @@ We also consider here a nano-hexapod with the identified optimal actuator stiffn
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org1575b3d" class="outline-4">
|
<div id="outline-container-org44ccdbe" class="outline-4">
|
||||||
<h4 id="org1575b3d"><span class="section-number-4">1.3.1</span> Direct Velocity Feedback</h4>
|
<h4 id="org44ccdbe"><span class="section-number-4">1.3.1</span> Direct Velocity Feedback</h4>
|
||||||
<div class="outline-text-4" id="text-1-3-1">
|
<div class="outline-text-4" id="text-1-3-1">
|
||||||
<p>
|
<p>
|
||||||
The dynamics from the actuators to the relative displacement sensor in each leg is identified and shown in Figure <a href="#org8fbbf9d">3</a>.
|
The dynamics from the actuators to the relative displacement sensor in each leg is identified and shown in Figure <a href="#org8fbbf9d">3</a>.
|
||||||
@@ -279,8 +279,8 @@ It is shown that the bending stiffness of the flexible joints does indeed change
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgb35fa00" class="outline-4">
|
<div id="outline-container-org5d9965b" class="outline-4">
|
||||||
<h4 id="orgb35fa00"><span class="section-number-4">1.3.2</span> Primary Control</h4>
|
<h4 id="org5d9965b"><span class="section-number-4">1.3.2</span> Primary Control</h4>
|
||||||
<div class="outline-text-4" id="text-1-3-2">
|
<div class="outline-text-4" id="text-1-3-2">
|
||||||
<p>
|
<p>
|
||||||
The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs) is shown in Figure <a href="#orgb739560">5</a>.
|
The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs) is shown in Figure <a href="#orgb739560">5</a>.
|
||||||
@@ -299,8 +299,8 @@ It is shown that the bending stiffness of the flexible joints have very little i
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org4a1264f" class="outline-4">
|
<div id="outline-container-org0f9f990" class="outline-4">
|
||||||
<h4 id="org4a1264f"><span class="section-number-4">1.3.3</span> Conclusion</h4>
|
<h4 id="org0f9f990"><span class="section-number-4">1.3.3</span> Conclusion</h4>
|
||||||
<div class="outline-text-4" id="text-1-3-3">
|
<div class="outline-text-4" id="text-1-3-3">
|
||||||
<div class="important">
|
<div class="important">
|
||||||
<p>
|
<p>
|
||||||
@@ -341,8 +341,8 @@ Cz_M = 1*ones(6,1); % [N/(m/s)]
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org14d57c4" class="outline-4">
|
<div id="outline-container-org8fdef7f" class="outline-4">
|
||||||
<h4 id="org14d57c4"><span class="section-number-4">2.1.1</span> Initialization</h4>
|
<h4 id="org8fdef7f"><span class="section-number-4">2.1.1</span> Initialization</h4>
|
||||||
<div class="outline-text-4" id="text-2-1-1">
|
<div class="outline-text-4" id="text-2-1-1">
|
||||||
<p>
|
<p>
|
||||||
Let’s initialize all the stages with default parameters.
|
Let’s initialize all the stages with default parameters.
|
||||||
@@ -370,8 +370,8 @@ initializeReferences('Rz_type', 'rotating-not-filtered', 'Rz_period', 60);
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org790d5e4" class="outline-4">
|
<div id="outline-container-orgc087bb9" class="outline-4">
|
||||||
<h4 id="org790d5e4"><span class="section-number-4">2.1.2</span> Direct Velocity Feedback</h4>
|
<h4 id="orgc087bb9"><span class="section-number-4">2.1.2</span> Direct Velocity Feedback</h4>
|
||||||
<div class="outline-text-4" id="text-2-1-2">
|
<div class="outline-text-4" id="text-2-1-2">
|
||||||
<p>
|
<p>
|
||||||
The dynamics from actuators force \(\tau_i\) to relative motion sensors \(d\mathcal{L}_i\) with and without considering the flexible joint stiffness are identified.
|
The dynamics from actuators force \(\tau_i\) to relative motion sensors \(d\mathcal{L}_i\) with and without considering the flexible joint stiffness are identified.
|
||||||
@@ -390,8 +390,8 @@ The obtained dynamics are shown in Figure <a href="#org78dd87a">6</a>.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgddae25e" class="outline-4">
|
<div id="outline-container-org4069e58" class="outline-4">
|
||||||
<h4 id="orgddae25e"><span class="section-number-4">2.1.3</span> Primary Plant</h4>
|
<h4 id="org4069e58"><span class="section-number-4">2.1.3</span> Primary Plant</h4>
|
||||||
<div class="outline-text-4" id="text-2-1-3">
|
<div class="outline-text-4" id="text-2-1-3">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">Kdvf = 5e3*s/(1+s/2/pi/1e3)*eye(6);
|
<pre class="src src-matlab">Kdvf = 5e3*s/(1+s/2/pi/1e3)*eye(6);
|
||||||
@@ -415,8 +415,8 @@ The dynamics is compare with and without the joint flexibility in Figure <a href
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org7ebf071" class="outline-4">
|
<div id="outline-container-org3d8a1a7" class="outline-4">
|
||||||
<h4 id="org7ebf071"><span class="section-number-4">2.1.4</span> Conclusion</h4>
|
<h4 id="org3d8a1a7"><span class="section-number-4">2.1.4</span> Conclusion</h4>
|
||||||
<div class="outline-text-4" id="text-2-1-4">
|
<div class="outline-text-4" id="text-2-1-4">
|
||||||
<div class="important">
|
<div class="important">
|
||||||
<p>
|
<p>
|
||||||
@@ -448,8 +448,8 @@ We also consider here a nano-hexapod with the identified optimal actuator stiffn
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org5ed48b8" class="outline-4">
|
<div id="outline-container-orgdb214f9" class="outline-4">
|
||||||
<h4 id="org5ed48b8"><span class="section-number-4">2.2.1</span> Direct Velocity Feedback</h4>
|
<h4 id="orgdb214f9"><span class="section-number-4">2.2.1</span> Direct Velocity Feedback</h4>
|
||||||
<div class="outline-text-4" id="text-2-2-1">
|
<div class="outline-text-4" id="text-2-2-1">
|
||||||
<p>
|
<p>
|
||||||
The dynamics from the actuators to the relative displacement sensor in each leg is identified and shown in Figure <a href="#orgab9ab86">8</a>.
|
The dynamics from the actuators to the relative displacement sensor in each leg is identified and shown in Figure <a href="#orgab9ab86">8</a>.
|
||||||
@@ -491,8 +491,8 @@ It can be seen that very little active damping can be achieve for axial stiffnes
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org5d9965b" class="outline-4">
|
<div id="outline-container-org53e5f08" class="outline-4">
|
||||||
<h4 id="org5d9965b"><span class="section-number-4">2.2.2</span> Primary Control</h4>
|
<h4 id="org53e5f08"><span class="section-number-4">2.2.2</span> Primary Control</h4>
|
||||||
<div class="outline-text-4" id="text-2-2-2">
|
<div class="outline-text-4" id="text-2-2-2">
|
||||||
<p>
|
<p>
|
||||||
The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs) is shown in Figure <a href="#org6070692">11</a>.
|
The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs) is shown in Figure <a href="#org6070692">11</a>.
|
||||||
@@ -508,8 +508,8 @@ The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org8ee81cd" class="outline-3">
|
<div id="outline-container-org1ddd8bf" class="outline-3">
|
||||||
<h3 id="org8ee81cd"><span class="section-number-3">2.3</span> Conclusion</h3>
|
<h3 id="org1ddd8bf"><span class="section-number-3">2.3</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-2-3">
|
<div class="outline-text-3" id="text-2-3">
|
||||||
<div class="important">
|
<div class="important">
|
||||||
<p>
|
<p>
|
||||||
@@ -533,8 +533,8 @@ We may interpolate the results and say that the axial joint stiffness should be
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgb8a9692" class="outline-2">
|
<div id="outline-container-orga32adf0" class="outline-2">
|
||||||
<h2 id="orgb8a9692"><span class="section-number-2">3</span> Conclusion</h2>
|
<h2 id="orga32adf0"><span class="section-number-2">3</span> Conclusion</h2>
|
||||||
<div class="outline-text-2" id="text-3">
|
<div class="outline-text-2" id="text-3">
|
||||||
<p>
|
<p>
|
||||||
<a id="org6614f42"></a>
|
<a id="org6614f42"></a>
|
||||||
@@ -556,7 +556,7 @@ For the identified optimal actuator stiffness \(k = 10^5\,[N/m]\), the flexible
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2020-05-05 mar. 10:44</p>
|
<p class="date">Created: 2020-05-05 mar. 11:26</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
@@ -6,12 +6,12 @@ In this document is studied the effect of the mechanical behavior of the flexibl
|
|||||||
|
|
||||||
Ideally, we want the x and y rotations to be free and all the translations to be blocked.
|
Ideally, we want the x and y rotations to be free and all the translations to be blocked.
|
||||||
However, this is never the case and be have to consider:
|
However, this is never the case and be have to consider:
|
||||||
- Finite x and y rotational stiffnesses (Section [[sec:rot_stiffness]])
|
- Finite bending stiffnesses (Section [[sec:rot_stiffness]])
|
||||||
- Translation stiffness in the direction of the legs (Section [[sec:trans_stiffness]])
|
- Axial stiffness in the direction of the legs (Section [[sec:trans_stiffness]])
|
||||||
|
|
||||||
This may impose some limitations, also, the goal is to specify the required joints stiffnesses.
|
This may impose some limitations, also, the goal is to specify the required joints stiffnesses (summarized in Section [[sec:conclusion]]).
|
||||||
|
|
||||||
* Rotational Stiffness
|
* Bending and Torsional Stiffness
|
||||||
<<sec:rot_stiffness>>
|
<<sec:rot_stiffness>>
|
||||||
|
|
||||||
** Introduction :ignore:
|
** Introduction :ignore:
|
||||||
@@ -67,7 +67,7 @@ Let's consider the heaviest mass which should we the most problematic with it co
|
|||||||
Kdvf = tf(zeros(6));
|
Kdvf = tf(zeros(6));
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Realistic Rotational Stiffness Values
|
** Realistic Bending Stiffness Values
|
||||||
*** Introduction :ignore:
|
*** Introduction :ignore:
|
||||||
Let's compare the ideal case (zero stiffness in rotation and infinite stiffness in translation) with a more realistic case:
|
Let's compare the ideal case (zero stiffness in rotation and infinite stiffness in translation) with a more realistic case:
|
||||||
- $K_{\theta, \phi} = 15\,[Nm/rad]$ stiffness in flexion
|
- $K_{\theta, \phi} = 15\,[Nm/rad]$ stiffness in flexion
|
||||||
@@ -231,7 +231,7 @@ The plant dynamics is not found to be changing significantly.
|
|||||||
end
|
end
|
||||||
for j = 1:6
|
for j = 1:6
|
||||||
set(gca,'ColorOrderIndex',2);
|
set(gca,'ColorOrderIndex',2);
|
||||||
plot(freqs, abs(squeeze(freqresp(Gl_p(j, j), freqs, 'Hz'))), '--');
|
plot(freqs, abs(squeeze(freqresp(Gl_p(j, j), freqs, 'Hz'))));
|
||||||
end
|
end
|
||||||
hold off;
|
hold off;
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
@@ -241,17 +241,30 @@ The plant dynamics is not found to be changing significantly.
|
|||||||
hold on;
|
hold on;
|
||||||
for j = 1:6
|
for j = 1:6
|
||||||
set(gca,'ColorOrderIndex',1);
|
set(gca,'ColorOrderIndex',1);
|
||||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gl(j, j), freqs, 'Hz')))));
|
if j == 1
|
||||||
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gl(j, j), freqs, 'Hz')))), ...
|
||||||
|
'DisplayName', 'Flexible Joints');
|
||||||
|
else
|
||||||
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gl(j, j), freqs, 'Hz')))), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
end
|
end
|
||||||
for j = 1:6
|
for j = 1:6
|
||||||
set(gca,'ColorOrderIndex',2);
|
set(gca,'ColorOrderIndex',2);
|
||||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gl_p(j, j), freqs, 'Hz')))), '--');
|
if j == 1
|
||||||
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gl_p(j, j), freqs, 'Hz')))), ...
|
||||||
|
'DisplayName', 'Perfect Joints');
|
||||||
|
else
|
||||||
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gl_p(j, j), freqs, 'Hz')))), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
end
|
end
|
||||||
hold off;
|
hold off;
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
ylim([-270, 90]);
|
ylim([-270, 90]);
|
||||||
yticks([-360:90:360]);
|
yticks([-360:90:360]);
|
||||||
|
legend('location', 'southwest');
|
||||||
|
|
||||||
linkaxes([ax1,ax2],'x');
|
linkaxes([ax1,ax2],'x');
|
||||||
#+end_src
|
#+end_src
|
||||||
@@ -261,13 +274,13 @@ The plant dynamics is not found to be changing significantly.
|
|||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+name: fig:flex_joints_rot_primary_plant_L
|
#+name: fig:flex_joints_rot_primary_plant_L
|
||||||
#+caption: Dynamics from $\bm{\tau}^\prime_i$ to $\bm{\epsilon}_{\mathcal{X}_n,i}$ with perfect joints (dashed) and with flexible joints (solid)
|
#+caption: Dynamics from $\bm{\tau}^\prime_i$ to $\bm{\epsilon}_{\mathcal{X}_n,i}$ with perfect joints and with flexible joints
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
[[file:figs/flex_joints_rot_primary_plant_L.png]]
|
[[file:figs/flex_joints_rot_primary_plant_L.png]]
|
||||||
|
|
||||||
*** Conclusion
|
*** Conclusion
|
||||||
#+begin_important
|
#+begin_important
|
||||||
Considering realistic flexible joint rotational stiffness for the nano-hexapod does not seems to impose any limitation on the DVF control nor on the primary control.
|
Considering realistic flexible joint bending stiffness for the nano-hexapod does not seems to impose any limitation on the DVF control nor on the primary control.
|
||||||
|
|
||||||
It only increases a little bit the suspension modes of the sample on top of the nano-hexapod.
|
It only increases a little bit the suspension modes of the sample on top of the nano-hexapod.
|
||||||
#+end_important
|
#+end_important
|
||||||
@@ -277,7 +290,7 @@ It only increases a little bit the suspension modes of the sample on top of the
|
|||||||
We wish now to see what is the impact of the rotation stiffness of the flexible joints on the dynamics.
|
We wish now to see what is the impact of the rotation stiffness of the flexible joints on the dynamics.
|
||||||
This will help to determine the requirements on the joint's stiffness.
|
This will help to determine the requirements on the joint's stiffness.
|
||||||
|
|
||||||
Let's consider the following rotational stiffness of the flexible joints:
|
Let's consider the following bending stiffness of the flexible joints:
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
Ks = [1, 5, 10, 50, 100]; % [Nm/rad]
|
Ks = [1, 5, 10, 50, 100]; % [Nm/rad]
|
||||||
#+end_src
|
#+end_src
|
||||||
@@ -294,7 +307,7 @@ The dynamics from the actuators to the relative displacement sensor in each leg
|
|||||||
|
|
||||||
The corresponding Root Locus plot is shown in Figure [[fig:flex_joints_rot_study_dvf_root_locus]].
|
The corresponding Root Locus plot is shown in Figure [[fig:flex_joints_rot_study_dvf_root_locus]].
|
||||||
|
|
||||||
It is shown that the rotational stiffness of the flexible joints does indeed change a little the dynamics, but critical damping is stiff achievable with Direct Velocity Feedback.
|
It is shown that the bending stiffness of the flexible joints does indeed change a little the dynamics, but critical damping is stiff achievable with Direct Velocity Feedback.
|
||||||
|
|
||||||
#+begin_src matlab :exports none
|
#+begin_src matlab :exports none
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
@@ -343,7 +356,7 @@ It is shown that the rotational stiffness of the flexible joints does indeed cha
|
|||||||
hold on;
|
hold on;
|
||||||
for i = 1:length(Ks)
|
for i = 1:length(Ks)
|
||||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_dvf_s{i}(1, 1), freqs, 'Hz')))), ...
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_dvf_s{i}(1, 1), freqs, 'Hz')))), ...
|
||||||
'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
|
'DisplayName', sprintf('$k = %.0f$ [Nm/rad]', Ks(i)));
|
||||||
end
|
end
|
||||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_dvf_p(1, 1), freqs, 'Hz')))), 'k--', ...
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_dvf_p(1, 1), freqs, 'Hz')))), 'k--', ...
|
||||||
'DisplayName', 'Ideal Joint');
|
'DisplayName', 'Ideal Joint');
|
||||||
@@ -375,7 +388,7 @@ It is shown that the rotational stiffness of the flexible joints does indeed cha
|
|||||||
for i = 1:length(Ks)
|
for i = 1:length(Ks)
|
||||||
set(gca,'ColorOrderIndex',i);
|
set(gca,'ColorOrderIndex',i);
|
||||||
plot(real(pole(G_dvf_s{i})), imag(pole(G_dvf_s{i})), 'x', ...
|
plot(real(pole(G_dvf_s{i})), imag(pole(G_dvf_s{i})), 'x', ...
|
||||||
'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
|
'DisplayName', sprintf('$k = %.0f$ [Nm/rad]', Ks(i)));
|
||||||
set(gca,'ColorOrderIndex',i);
|
set(gca,'ColorOrderIndex',i);
|
||||||
plot(real(tzero(G_dvf_s{i})), imag(tzero(G_dvf_s{i})), 'o', ...
|
plot(real(tzero(G_dvf_s{i})), imag(tzero(G_dvf_s{i})), 'o', ...
|
||||||
'HandleVisibility', 'off');
|
'HandleVisibility', 'off');
|
||||||
@@ -406,7 +419,7 @@ It is shown that the rotational stiffness of the flexible joints does indeed cha
|
|||||||
*** Primary Control
|
*** Primary Control
|
||||||
The dynamics from $\bm{\tau}^\prime$ to $\bm{\epsilon}_{\mathcal{X}_n}$ (for the primary controller designed in the frame of the legs) is shown in Figure [[fig:flex_joints_rot_study_primary_plant]].
|
The dynamics from $\bm{\tau}^\prime$ to $\bm{\epsilon}_{\mathcal{X}_n}$ (for the primary controller designed in the frame of the legs) is shown in Figure [[fig:flex_joints_rot_study_primary_plant]].
|
||||||
|
|
||||||
It is shown that the rotational stiffness of the flexible joints have very little impact on the dynamics.
|
It is shown that the bending stiffness of the flexible joints have very little impact on the dynamics.
|
||||||
|
|
||||||
#+begin_src matlab :exports none
|
#+begin_src matlab :exports none
|
||||||
Kdvf = 5e3*s/(1+s/2/pi/1e3)*eye(6);
|
Kdvf = 5e3*s/(1+s/2/pi/1e3)*eye(6);
|
||||||
@@ -463,7 +476,7 @@ It is shown that the rotational stiffness of the flexible joints have very littl
|
|||||||
hold on;
|
hold on;
|
||||||
for i = 1:length(Ks)
|
for i = 1:length(Ks)
|
||||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gl_s{i}(1, 1), freqs, 'Hz')))), ...
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gl_s{i}(1, 1), freqs, 'Hz')))), ...
|
||||||
'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
|
'DisplayName', sprintf('$k = %.0f$ [Nm/rad]', Ks(i)));
|
||||||
end
|
end
|
||||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gl_p(1, 1), freqs, 'Hz')))), 'k--', ...
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gl_p(1, 1), freqs, 'Hz')))), 'k--', ...
|
||||||
'DisplayName', 'Ideal Joint');
|
'DisplayName', 'Ideal Joint');
|
||||||
@@ -482,13 +495,13 @@ It is shown that the rotational stiffness of the flexible joints have very littl
|
|||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+name: fig:flex_joints_rot_study_primary_plant
|
#+name: fig:flex_joints_rot_study_primary_plant
|
||||||
#+caption: Diagonal elements of the transfer function matrix from $\bm{\tau}^\prime$ to $\bm{\epsilon}_{\mathcal{X}_n}$ for the considered rotational stiffnesses
|
#+caption: Diagonal elements of the transfer function matrix from $\bm{\tau}^\prime$ to $\bm{\epsilon}_{\mathcal{X}_n}$ for the considered bending stiffnesses
|
||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
[[file:figs/flex_joints_rot_study_primary_plant.png]]
|
[[file:figs/flex_joints_rot_study_primary_plant.png]]
|
||||||
|
|
||||||
*** Conclusion
|
*** Conclusion
|
||||||
#+begin_important
|
#+begin_important
|
||||||
The rotational stiffness of the flexible joint does not significantly change the dynamics.
|
The bending stiffness of the flexible joint does not significantly change the dynamics.
|
||||||
#+end_important
|
#+end_important
|
||||||
|
|
||||||
* Translation Stiffness
|
* Translation Stiffness
|
||||||
@@ -735,6 +748,11 @@ The dynamics is compare with and without the joint flexibility in Figure [[fig:f
|
|||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
[[file:figs/flex_joints_trans_primary_plant_L.png]]
|
[[file:figs/flex_joints_trans_primary_plant_L.png]]
|
||||||
|
|
||||||
|
*** Conclusion
|
||||||
|
#+begin_important
|
||||||
|
For the realistic value of the flexible joint axial stiffness, the dynamics is not much impact, and this should not be a problem for control.
|
||||||
|
#+end_important
|
||||||
|
|
||||||
** Parametric study
|
** Parametric study
|
||||||
*** Introduction :ignore:
|
*** Introduction :ignore:
|
||||||
We wish now to see what is the impact of the *axial* stiffness of the flexible joints on the dynamics.
|
We wish now to see what is the impact of the *axial* stiffness of the flexible joints on the dynamics.
|
||||||
@@ -759,7 +777,7 @@ It is shown that the axial stiffness of the flexible joints does have a huge imp
|
|||||||
If the axial stiffness of the flexible joints is $K_a > 10^7\,[N/m]$ (here $100$ times higher than the actuator stiffness), then the change of dynamics stays reasonably small.
|
If the axial stiffness of the flexible joints is $K_a > 10^7\,[N/m]$ (here $100$ times higher than the actuator stiffness), then the change of dynamics stays reasonably small.
|
||||||
|
|
||||||
This is more clear by looking at the root locus (Figures [[fig:flex_joints_trans_study_dvf_root_locus]] and [[fig:flex_joints_trans_study_root_locus_unzoom]]).
|
This is more clear by looking at the root locus (Figures [[fig:flex_joints_trans_study_dvf_root_locus]] and [[fig:flex_joints_trans_study_root_locus_unzoom]]).
|
||||||
It can be seen that very little active damping can be achieve for rotational joint axial stiffnesses below $10^7\,[N/m]$.
|
It can be seen that very little active damping can be achieve for axial stiffnesses below $10^7\,[N/m]$.
|
||||||
|
|
||||||
#+begin_src matlab :exports none
|
#+begin_src matlab :exports none
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
@@ -868,7 +886,7 @@ It can be seen that very little active damping can be achieve for rotational joi
|
|||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
[[file:figs/flex_joints_trans_study_dvf_root_locus.png]]
|
[[file:figs/flex_joints_trans_study_dvf_root_locus.png]]
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab :exports none
|
||||||
xlim([-1e3, 0]);
|
xlim([-1e3, 0]);
|
||||||
ylim([0, 1e3]);
|
ylim([0, 1e3]);
|
||||||
#+end_src
|
#+end_src
|
||||||
@@ -964,9 +982,19 @@ The dynamics from $\bm{\tau}^\prime$ to $\bm{\epsilon}_{\mathcal{X}_n}$ (for the
|
|||||||
#+begin_important
|
#+begin_important
|
||||||
The axial stiffness of the flexible joints should be maximized.
|
The axial stiffness of the flexible joints should be maximized.
|
||||||
|
|
||||||
For the considered actuator stiffness $k = 10^5\,[N/m]$, the axial stiffness of the rotational joints should ideally be above $10^7\,[N/m]$.
|
For the considered actuator stiffness $k = 10^5\,[N/m]$, the axial stiffness of the flexible joints should ideally be above $10^7\,[N/m]$.
|
||||||
|
|
||||||
This is a reasonable stiffness value for such joints.
|
This is a reasonable stiffness value for such joints.
|
||||||
|
|
||||||
We may interpolate the results and say that the axial joint stiffness should be 100 times higher than the actuator stiffness, but this should be confirmed with further analysis.
|
We may interpolate the results and say that the axial joint stiffness should be 100 times higher than the actuator stiffness, but this should be confirmed with further analysis.
|
||||||
#+end_important
|
#+end_important
|
||||||
|
|
||||||
|
* Conclusion
|
||||||
|
<<sec:conclusion>>
|
||||||
|
|
||||||
|
#+begin_important
|
||||||
|
For the identified optimal actuator stiffness $k = 10^5\,[N/m]$, the flexible joint should have the following stiffness properties:
|
||||||
|
- Bending Stiffness: $K_b < 50\,[Nm/rad]$
|
||||||
|
- Torsion Stiffness: $K_t < 50\,[Nm/rad]$
|
||||||
|
- Axial Stiffness: $K_a > 10^7\,[N/m]$
|
||||||
|
#+end_important
|
||||||
|
|||||||
@@ -65,6 +65,10 @@ Conclusion are drawn about what experimental conditions are critical on the vari
|
|||||||
|
|
||||||
* Optimal Stiffness of the nano-hexapod to reduce plant uncertainty ([[file:uncertainty_optimal_stiffness.org][link]])
|
* Optimal Stiffness of the nano-hexapod to reduce plant uncertainty ([[file:uncertainty_optimal_stiffness.org][link]])
|
||||||
|
|
||||||
|
* Effect of flexible joints on the plant dynamics ([[file:flexible_joints_study.org][link]])
|
||||||
|
In this document is studied how the flexible joint stiffnesses (in flexion, torsion and compression) is affecting the plant dynamics.
|
||||||
|
Conclusion are drawn on the required stiffness properties of the flexible joints.
|
||||||
|
|
||||||
* Active Damping Techniques on the full Simscape Model ([[file:control_active_damping.org][link]])
|
* Active Damping Techniques on the full Simscape Model ([[file:control_active_damping.org][link]])
|
||||||
Active damping techniques are applied to the full Simscape model.
|
Active damping techniques are applied to the full Simscape model.
|
||||||
|
|
||||||
|
|||||||
@@ -25,7 +25,7 @@
|
|||||||
|
|
||||||
#+PROPERTY: header-args:shell :eval no-export
|
#+PROPERTY: header-args:shell :eval no-export
|
||||||
|
|
||||||
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
|
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}")
|
||||||
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
|
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
|
||||||
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
|
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
|
||||||
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
|
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
|
||||||
|
|||||||
@@ -11,10 +11,14 @@ function [stewart] = initializeJointDynamics(stewart, args)
|
|||||||
% - Kt_M [6x1] - Torsion (Rz) Stiffness for each top joints [(N.m)/rad]
|
% - Kt_M [6x1] - Torsion (Rz) Stiffness for each top joints [(N.m)/rad]
|
||||||
% - Cf_M [6x1] - Bending (Rx, Ry) Damping of each top joint [(N.m)/(rad/s)]
|
% - Cf_M [6x1] - Bending (Rx, Ry) Damping of each top joint [(N.m)/(rad/s)]
|
||||||
% - Ct_M [6x1] - Torsion (Rz) Damping of each top joint [(N.m)/(rad/s)]
|
% - Ct_M [6x1] - Torsion (Rz) Damping of each top joint [(N.m)/(rad/s)]
|
||||||
|
% - Kz_M [6x1] - Translation (Tz) Stiffness for each top joints [N/m]
|
||||||
|
% - Cz_M [6x1] - Translation (Tz) Damping of each top joint [N/m]
|
||||||
% - Kf_F [6x1] - Bending (Rx, Ry) Stiffness for each bottom joints [(N.m)/rad]
|
% - Kf_F [6x1] - Bending (Rx, Ry) Stiffness for each bottom joints [(N.m)/rad]
|
||||||
% - Kt_F [6x1] - Torsion (Rz) Stiffness for each bottom joints [(N.m)/rad]
|
% - Kt_F [6x1] - Torsion (Rz) Stiffness for each bottom joints [(N.m)/rad]
|
||||||
% - Cf_F [6x1] - Bending (Rx, Ry) Damping of each bottom joint [(N.m)/(rad/s)]
|
% - Cf_F [6x1] - Bending (Rx, Ry) Damping of each bottom joint [(N.m)/(rad/s)]
|
||||||
% - Cf_F [6x1] - Torsion (Rz) Damping of each bottom joint [(N.m)/(rad/s)]
|
% - Cf_F [6x1] - Torsion (Rz) Damping of each bottom joint [(N.m)/(rad/s)]
|
||||||
|
% - Kz_F [6x1] - Translation (Tz) Stiffness for each bottom joints [N/m]
|
||||||
|
% - Cz_F [6x1] - Translation (Tz) Damping of each bottom joint [N/m]
|
||||||
%
|
%
|
||||||
% Outputs:
|
% Outputs:
|
||||||
% - stewart - updated Stewart structure with the added fields:
|
% - stewart - updated Stewart structure with the added fields:
|
||||||
@@ -29,16 +33,20 @@ function [stewart] = initializeJointDynamics(stewart, args)
|
|||||||
|
|
||||||
arguments
|
arguments
|
||||||
stewart
|
stewart
|
||||||
args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p'})} = 'universal'
|
args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p', 'universal_3dof'})} = 'universal'
|
||||||
args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p'})} = 'spherical'
|
args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p', 'spherical_3dof'})} = 'spherical'
|
||||||
args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
|
args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
|
||||||
args.Cf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
|
args.Cf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
|
||||||
args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
|
args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
|
||||||
args.Ct_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
|
args.Ct_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
|
||||||
|
args.Kz_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 60e6*ones(6,1)
|
||||||
|
args.Cz_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e2*ones(6,1)
|
||||||
args.Kf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
|
args.Kf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
|
||||||
args.Cf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
|
args.Cf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
|
||||||
args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
|
args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
|
||||||
args.Ct_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
|
args.Ct_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
|
||||||
|
args.Kz_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 60e6*ones(6,1)
|
||||||
|
args.Cz_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e2*ones(6,1)
|
||||||
end
|
end
|
||||||
|
|
||||||
switch args.type_F
|
switch args.type_F
|
||||||
@@ -50,6 +58,8 @@ switch args.type_F
|
|||||||
stewart.joints_F.type = 3;
|
stewart.joints_F.type = 3;
|
||||||
case 'spherical_p'
|
case 'spherical_p'
|
||||||
stewart.joints_F.type = 4;
|
stewart.joints_F.type = 4;
|
||||||
|
case 'universal_3dof'
|
||||||
|
stewart.joints_F.type = 5;
|
||||||
end
|
end
|
||||||
|
|
||||||
switch args.type_M
|
switch args.type_M
|
||||||
@@ -61,23 +71,25 @@ switch args.type_M
|
|||||||
stewart.joints_M.type = 3;
|
stewart.joints_M.type = 3;
|
||||||
case 'spherical_p'
|
case 'spherical_p'
|
||||||
stewart.joints_M.type = 4;
|
stewart.joints_M.type = 4;
|
||||||
|
case 'spherical_3dof'
|
||||||
|
stewart.joints_M.type = 6;
|
||||||
end
|
end
|
||||||
|
|
||||||
stewart.joints_M.Kx = zeros(6,1);
|
stewart.joints_M.Kx = zeros(6,1);
|
||||||
stewart.joints_M.Ky = zeros(6,1);
|
stewart.joints_M.Ky = zeros(6,1);
|
||||||
stewart.joints_M.Kz = zeros(6,1);
|
stewart.joints_M.Kz = args.Kz_M;
|
||||||
|
|
||||||
stewart.joints_F.Kx = zeros(6,1);
|
stewart.joints_F.Kx = zeros(6,1);
|
||||||
stewart.joints_F.Ky = zeros(6,1);
|
stewart.joints_F.Ky = zeros(6,1);
|
||||||
stewart.joints_F.Kz = zeros(6,1);
|
stewart.joints_F.Kz = args.Kz_F;
|
||||||
|
|
||||||
stewart.joints_M.Cx = zeros(6,1);
|
stewart.joints_M.Cx = zeros(6,1);
|
||||||
stewart.joints_M.Cy = zeros(6,1);
|
stewart.joints_M.Cy = zeros(6,1);
|
||||||
stewart.joints_M.Cz = zeros(6,1);
|
stewart.joints_M.Cz = args.Cz_M;
|
||||||
|
|
||||||
stewart.joints_F.Cx = zeros(6,1);
|
stewart.joints_F.Cx = zeros(6,1);
|
||||||
stewart.joints_F.Cy = zeros(6,1);
|
stewart.joints_F.Cy = zeros(6,1);
|
||||||
stewart.joints_F.Cz = zeros(6,1);
|
stewart.joints_F.Cz = args.Cz_F;
|
||||||
|
|
||||||
stewart.joints_M.Kf = args.Kf_M;
|
stewart.joints_M.Kf = args.Kf_M;
|
||||||
stewart.joints_M.Kt = args.Kf_M;
|
stewart.joints_M.Kt = args.Kf_M;
|
||||||
|
|||||||
@@ -17,16 +17,20 @@ arguments
|
|||||||
args.k (1,1) double {mustBeNumeric} = -1
|
args.k (1,1) double {mustBeNumeric} = -1
|
||||||
args.c (1,1) double {mustBeNumeric} = -1
|
args.c (1,1) double {mustBeNumeric} = -1
|
||||||
% initializeJointDynamics
|
% initializeJointDynamics
|
||||||
args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p'})} = 'universal'
|
args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p', 'universal_3dof'})} = 'universal'
|
||||||
args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p'})} = 'spherical'
|
args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p', 'spherical_3dof'})} = 'spherical'
|
||||||
args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
|
args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
|
||||||
args.Cf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
|
args.Cf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
|
||||||
args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
|
args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
|
||||||
args.Ct_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
|
args.Ct_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
|
||||||
|
args.Kz_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 60e6*ones(6,1)
|
||||||
|
args.Cz_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e2*ones(6,1)
|
||||||
args.Kf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
|
args.Kf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
|
||||||
args.Cf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
|
args.Cf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
|
||||||
args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
|
args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
|
||||||
args.Ct_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
|
args.Ct_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
|
||||||
|
args.Kz_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 60e6*ones(6,1)
|
||||||
|
args.Cz_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e2*ones(6,1)
|
||||||
% initializeCylindricalPlatforms
|
% initializeCylindricalPlatforms
|
||||||
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 1
|
||||||
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
|
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
|
||||||
@@ -77,10 +81,14 @@ stewart = initializeJointDynamics(stewart, ...
|
|||||||
'Cf_M' , args.Cf_M, ...
|
'Cf_M' , args.Cf_M, ...
|
||||||
'Kt_M' , args.Kt_M, ...
|
'Kt_M' , args.Kt_M, ...
|
||||||
'Ct_M' , args.Ct_M, ...
|
'Ct_M' , args.Ct_M, ...
|
||||||
|
'Kz_M' , args.Kz_M, ...
|
||||||
|
'Cz_M' , args.Cz_M, ...
|
||||||
'Kf_F' , args.Kf_F, ...
|
'Kf_F' , args.Kf_F, ...
|
||||||
'Cf_F' , args.Cf_F, ...
|
'Cf_F' , args.Cf_F, ...
|
||||||
'Kt_F' , args.Kt_F, ...
|
'Kt_F' , args.Kt_F, ...
|
||||||
'Ct_F' , args.Ct_F);
|
'Ct_F' , args.Ct_F, ...
|
||||||
|
'Kz_F' , args.Kz_F, ...
|
||||||
|
'Cz_F' , args.Cz_F);
|
||||||
|
|
||||||
stewart = initializeCylindricalPlatforms(stewart, 'Fpm', args.Fpm, 'Fph', args.Fph, 'Fpr', args.Fpr, 'Mpm', args.Mpm, 'Mph', args.Mph, 'Mpr', args.Mpr);
|
stewart = initializeCylindricalPlatforms(stewart, 'Fpm', args.Fpm, 'Fph', args.Fph, 'Fpr', args.Fpr, 'Mpm', args.Mpm, 'Mph', args.Mph, 'Mpr', args.Mpr);
|
||||||
|
|
||||||
|
|||||||
Reference in New Issue
Block a user