Stéphane on Locomotion - Comments: Stability of Surface Contacts for Humanoid Robotshttps://scaron.info/publications/icra-2015.html/2015-05-31T16:42:00+02:00Posted by: Stéphane2015-05-31T16:42:00+02:002015-05-31T16:42:00+02:00Stéphanetag:scaron.info,2015-05-31:/publications/icra-2015.html//comment-reply-assume-horizontal-floor<p>The condition holds for any contact orientation, be it a foot on the floor, a hand on a wall, etc. What Equations (18) and (19) assume is a planar contact area between the robot's end-effector and the environment. This area can have an arbitrary orientation with respect to the inertial …</p><p>The condition holds for any contact orientation, be it a foot on the floor, a hand on a wall, etc. What Equations (18) and (19) assume is a planar contact area between the robot's end-effector and the environment. This area can have an arbitrary orientation with respect to the inertial frame.</p> Posted by: Stéphane2015-05-31T16:42:00+02:002015-05-31T16:42:00+02:00Stéphanetag:scaron.info,2015-05-31:/publications/icra-2015.html//comment-reply-yaw-torque-critical<p>We can enumerate all cases by reformulating the yaw-moment condition at the CoP, as shown in p. 82 of <a class="reference external" href="https://scaron.info/papers/thesis.pdf">this manuscript</a>. This equivalent condition can be written:</p> <div class="math"> \begin{equation*} | \tau^z - \tau^z_\mathit{safe} | \leq \mu \, f^z \, d(\mathit{CoP}, \mathit{edge}) \end{equation*} </div> <p>where <span class="math">$$\tau^z_\mathit …</span></p><p>We can enumerate all cases by reformulating the yaw-moment condition at the CoP, as shown in p. 82 of <a class="reference external" href="https://scaron.info/papers/thesis.pdf">this manuscript</a>. This equivalent condition can be written:</p> <div class="math"> \begin{equation*} | \tau^z - \tau^z_\mathit{safe} | \leq \mu \, f^z \, d(\mathit{CoP}, \mathit{edge}) \end{equation*} </div> <p>where <span class="math">\(\tau^z_\mathit{safe}$$</span> is the yaw torque furthest away from inequality constraints (its formula is given in the manuscript), <span class="math">$$\mu$$</span> is the friction coefficient, <span class="math">$$f^z$$</span> is the normal contact force, and <span class="math">$$d(\mathit{CoP}, \mathit{edge})$$</span> is the distance from the CoP to the nearest edge of the contact area.</p> <p>Hence, there are three cases where this constraint becomes easier to violate:</p> <ol class="arabic simple"> <li>Friction is low</li> <li>Normal force at contact is low, <em>e.g.</em>, the robot is about to lift its foot</li> <li>CoP is close to the edge of the contact area</li> </ol> <p>The last condition typically depends on your trajectory optimization: if you lower-bound your <span class="math">$$d(\mathit{CoP}, \mathit{edge})$$</span> by other means, you may get a yaw-moment range <span class="math">$$\mu \, f^z \, d(\mathit{CoP}, \mathit{edge})$$</span> so large that you don't need to consider the yaw constraint explicitly. One example of this are the successive MPC implementations from Nicola Scianca <em>et al.</em>: <a class="reference external" href="https://www.youtube.com/watch?v=hYegqFoeCJc">initially</a> CoPs from their trajectory optimization were on the edge of their contact areas, but in a <a class="reference external" href="https://www.youtube.com/watch?v=cC92OdUSBME">later implementation</a> they constrained the CoP to be close to a point well inside the area. The former was much more sensitive to yaw slippage than the latter.</p> Posted by: Stéphane2015-05-31T16:42:00+02:002015-05-31T16:42:00+02:00Stéphanetag:scaron.info,2015-05-31:/publications/icra-2015.html//comment-reply-total-wrench-representation<p>The wrench <span class="math">$$\bfw = (\bff, \bftau)$$</span> in Proposition 2 is expressed at the central frame of the rectangular contact area. This frame has:</p> <ul class="simple"> <li>Its origin at the center <span class="math">$$O$$</span> of the area (depicted in Fig. 2(B))</li> <li>Its <span class="math">$$x$$</span>-axis aligned with the long axis of the rectangular contact area (hence …</li></ul><p>The wrench <span class="math">$$\bfw = (\bff, \bftau)$$</span> in Proposition 2 is expressed at the central frame of the rectangular contact area. This frame has:</p> <ul class="simple"> <li>Its origin at the center <span class="math">$$O$$</span> of the area (depicted in Fig. 2(B))</li> <li>Its <span class="math">$$x$$</span>-axis aligned with the long axis of the rectangular contact area (hence the half-length of the rectangle denoted by <span class="math">$$X$$</span>)</li> <li>Its <span class="math">$$y$$</span>-axis aligned with the short axis of the rectangular contact area (hence the half-width of the rectangle denoted by <span class="math">$$Y$$</span>)</li> <li>Its <span class="math">$$z$$</span>-axis aligned with the contact normal, pointing from the environment to the robot's end-effector.</li> </ul> Posted by: Attendee #32015-05-31T16:03:00+02:002015-05-31T16:03:00+02:00Attendee #3tag:scaron.info,2015-05-31:/publications/icra-2015.html//comment-question-yaw-torque-critical<p>For which application cases do you think additionally constraining the yaw torque becomes crucial, or the other way round, when is it also sufficient to only constrain the friction cone and CoP (e.g static/dynamic walking, highly-dynamic maneuvers)?</p>Posted by: Attendee #22015-05-31T16:02:00+02:002015-05-31T16:02:00+02:00Attendee #2tag:scaron.info,2015-05-31:/publications/icra-2015.html//comment-question-assume-horizontal-floor<p>Do the CoP Equations (18) and (19) assume a horizontal floor? Or does the contact wrench condition also hold for inclined contacts?</p>Posted by: Attendee #12015-05-31T16:01:00+02:002015-05-31T16:01:00+02:00Attendee #1tag:scaron.info,2015-05-31:/publications/icra-2015.html//comment-question-total-wrench-representation<p>Is the total wrench expressed as a spatial force in link coordinates of the contact, or as a Cartesian force in world coordinates?</p>