(leg_angles, leg_id)
return J
Computes the analytical Jacobian.
  Args:
  ` leg_angles: a list of 3 numbers for current abduction, hip and knee angle.
    l_hip_sign: whether it's a left (1) or right(-1) leg.
Computes the analytical Jacobian.
  Args:
  ` leg_angles: a list of 3 numbers for current abduction, hip and knee angle.
    l_hip_sign: whether it's a left (1) or right(-1) leg.
Computes the analytical Jacobian . Args : leg_angles : a list of 3 numbers for current abduction hip and knee angle . l_hip_sign : whether it s a left ( 1 ) or right ( - 1 ) leg .
def analytical_leg_jacobian(leg_angles, leg_id):
  """
  Computes the analytical Jacobian.
  Args:
  ` leg_angles: a list of 3 numbers for current abduction, hip and knee angle.
    l_hip_sign: whether it's a left (1) or right(-1) leg.
  """
  l_up = 0.2
  l_low = 0.2
  l_hip = 0.08505 * (-1)**(leg_id + 1)

  t1, t2, t3 = leg_angles[0], leg_angles[1], leg_angles[2]
  l_eff = np.sqrt(l_up**2 + l_low**2 + 2 * l_up * l_low * np.cos(t3))
  t_eff = t2 + t3 / 2
  J = np.zeros((3, 3))
  J[0, 0] = 0
  J[0, 1] = -l_eff * np.cos(t_eff)
  J[0, 2] = l_low * l_up * np.sin(t3) * np.sin(t_eff) / l_eff - l_eff * np.cos(
      t_eff) / 2
  J[1, 0] = -l_hip * np.sin(t1) + l_eff * np.cos(t1) * np.cos(t_eff)
  J[1, 1] = -l_eff * np.sin(t1) * np.sin(t_eff)
  J[1, 2] = -l_low * l_up * np.sin(t1) * np.sin(t3) * np.cos(
      t_eff) / l_eff - l_eff * np.sin(t1) * np.sin(t_eff) / 2
  J[2, 0] = l_hip * np.cos(t1) + l_eff * np.sin(t1) * np.cos(t_eff)
  J[2, 1] = l_eff * np.sin(t_eff) * np.cos(t1)
  J[2, 2] = l_low * l_up * np.sin(t3) * np.cos(t1) * np.cos(
      t_eff) / l_eff + l_eff * np.sin(t_eff) * np.cos(t1) / 2
  return J
def analytical_leg_jacobian ( leg_angles , leg_id ) : l_up = 0.2 l_low = 0.2 l_hip = 0.08505 * ( - 1 ) ** ( leg_id + 1 ) t1 , t2 , t3 = leg_angles [ 0 ] , leg_angles [ 1 ] , leg_angles [ 2 ] l_eff = np . sqrt ( l_up ** 2 + l_low ** 2 + 2 * l_up * l_low * np . cos ( t3 ) ) t_eff = t2 + t3 / 2 J = np . zeros ( ( 3 , 3 ) ) J [ 0 , 0 ] = 0 J [ 0 , 1 ] = - l_eff * np . cos ( t_eff ) J [ 0 , 2 ] = l_low * l_up * np . sin ( t3 ) * np . sin ( t_eff ) / l_eff - l_eff * np . cos ( t_eff ) / 2 J [ 1 , 0 ] = - l_hip * np . sin ( t1 ) + l_eff * np . cos ( t1 ) * np . cos ( t_eff ) J [ 1 , 1 ] = - l_eff * np . sin ( t1 ) * np . sin ( t_eff ) J [ 1 , 2 ] = - l_low * l_up * np . sin ( t1 ) * np . sin ( t3 ) * np . cos ( t_eff ) / l_eff - l_eff * np . sin ( t1 ) * np . sin ( t_eff ) / 2 J [ 2 , 0 ] = l_hip * np . cos ( t1 ) + l_eff * np . sin ( t1 ) * np . cos ( t_eff ) J [ 2 , 1 ] = l_eff * np . sin ( t_eff ) * np . cos ( t1 ) J [ 2 , 2 ] = l_low * l_up * np . sin ( t3 ) * np . cos ( t1 ) * np . cos ( t_eff ) / l_eff + l_eff * np . sin ( t_eff ) * np . cos ( t1 ) / 2 return J