better docs for ellipsoids

auctus-team · Aug 22, 2023 · db8cabe · db8cabe
1 parent 4e08735
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Showing 2 changed files with 31 additions and 7 deletions.
diff --git a/pycapacity/human.py b/pycapacity/human.py
@@ -26,12 +26,16 @@ def velocity_ellipsoid(J, N, dl_max):
     """
     Human musculoskeletal velocity ellipsoid calculation
 
-    .. math:: E_f = \{\dot{x}~ |~ J\dot{q} = \dot{x},~ L\dot{q} = \dot{l} \quad ||\dot{l}|| \leq \dot{l}_{max}\}
+    .. math:: E_f = \{\dot{x}~ |~ J\dot{q} = \dot{x},~ L\dot{q} = W=\dot{l} \quad ||W^{-1}\dot{l}|| \leq 1\}
+
+    where
 
+    .. math:: W=diag(\dot{l}_{max})
+
     Args:
         J: position jacobian
         N: moment arm matrix (:math:`N = -L^T`, where :math:`L` is the muscle length jacobian)
-        dl_max:  maximal joint velocities
+        dl_max:  maximal joint velocities 
 
     Returns
     ---------
@@ -53,7 +57,11 @@ def acceleration_ellipsoid(J, M, N, F_max):
     """
     Human muscuskeletal acceleration ellipsoid calculation (dynamic manipulability ellipsoid)
 
-    .. math:: E_a = \{\ddot{x}~ |~ \ddot{x} = JM^{-1}NF, \quad ||F|| \leq {F}_{max}\}
+    .. math:: E_a = \{\ddot{x}~ |~ \ddot{x} = JM^{-1}NF, \quad |W^{-1}|F|| \leq 1\}
+
+    where
+
+    .. math:: W=diag(F_{max})
 
     Args:
         J: matrix jacobian
@@ -80,8 +88,12 @@ def force_ellipsoid(J, N, F_max):
     """
     Human muscuskeletal force ellipsoid calculation
 
-    .. math:: E_f = \{f~ |~ NF  = J^Tf,\quad ||F|| \leq {F}_{max}\}
+    .. math:: E_f = \{f~ |~ NF  = J^Tf,\quad ||W^{-1}F|| \leq 1\}
+
+    where
 
+    .. math:: W=diag(F_{max})
+
     Args:
         J: matrix jacobian
         N: moment arm matrix

diff --git a/pycapacity/robot.py b/pycapacity/robot.py
@@ -27,7 +27,11 @@ def velocity_ellipsoid(J, dq_max):
     """
     Velocity manipulability ellipsoid calculation
 
-    .. math:: E_f = \{\dot{x}~ |~ J\dot{q} = \dot{x},\quad ||\dot{q}|| \leq \dot{q}_{max}\}
+    .. math:: E_f = \{\dot{x}~ |~ J\dot{q} = \dot{x},\quad ||W^{-1}\dot{q}|| \leq 1\}
+
+    where
+
+    .. math:: W=diag(\dot{q}_{max})
 
     Args:
         J: position jacobian
@@ -53,7 +57,11 @@ def acceleration_ellipsoid(J, M, t_max):
     """
     Acceleration ellipsoid calculation (dynamic manipulability ellipsoid)
 
-    .. math:: E_a = \{\ddot{x}~ |~ \ddot{x} = JM^{-1}\\tau,\quad ||{\\tau}|| \leq {\\tau}_{max}\}
+    .. math:: E_a = \{\ddot{x}~ |~ \ddot{x} = JM^{-1}\\tau,\quad ||W^{-1}{\\tau}|| \leq 1\}
+
+    where
+
+    .. math:: W=diag(\\tau_{max})
 
     Args:
         J: matrix jacobian
@@ -79,7 +87,11 @@ def force_ellipsoid(J, t_max):
     """
     Force manipulability ellipsoid calculation
 
-    .. math:: E_f = \{f~ |~ \\tau  = J^Tf,\quad ||\\tau|| \leq {\\tau}_{max}\}
+    .. math:: E_f = \{f~ |~ \\tau  = J^Tf,\quad ||W^{-1}\\tau|| \leq 1\}
+
+    where
+
+    .. math:: W=diag(\\tau_{max})
 
     Args:
         J: matrix jacobian