[Examples] Add example on how to use kinematics derivatives in Python

C++ example is coming soon.

examples/python/kinematics-derivatives.py

+import pinocchio as pin
+import numpy as np
+
+# Create model and data
+
+model = pin.Model.BuildHumanoidSimple()
+data = model.createData()
+
+# Set bounds (by default they are undefinded)
+
+model.lowerPositionLimit = -np.matrix(np.ones((model.nq,1)))
+model.upperPositionLimit = np.matrix(np.ones((model.nq,1)))
+
+q = pin.randomConfiguration(model) # joint configuration
+v = np.matrix(np.random.rand(model.nv,1)) # joint velocity
+a = np.matrix(np.random.rand(model.nv,1)) # joint acceleration
+
+# Evaluate all the terms required by the kinematics derivatives
+
+pin.computeForwardKinematicsDerivatives(model,data,q,v,a)
+
+# Evaluate the derivatives for a precise joint (e.g. rleg6_joint)
+
+joint_name = "rleg6_joint"
+joint_id = model.getJointId(joint_name)
+
+# Derivatives of the spatial velocity with respect to the joint configuration and velocity vectors
+
+(dv_dq,dv_dv) = pin.getJointVelocityDerivatives(model,data,joint_id,pin.ReferenceFrame.WORLD)
+# or to get them in the LOCAL frame of the joint
+(dv_dq_local,dv_dv_local) = pin.getJointVelocityDerivatives(model,data,joint_id,pin.ReferenceFrame.LOCAL)
+
+# Derivatives of the spatial acceleration of the joint with respect to the joint configuration, velocity and acceleration vectors
+
+(dv_dq,da_dq,da_dv,da_da) = pin.getJointAccelerationDerivatives(model,data,joint_id,pin.ReferenceFrame.WORLD)
+# or to get them in the LOCAL frame of the joint
+(dv_dq_local,da_dq_local,da_dv_local,da_da_local) = pin.getJointAccelerationDerivatives(model,data,joint_id,pin.ReferenceFrame.LOCAL)