momentumopt.kinoptpy.lqr_gain_manifold.CentroidalLqr Class Reference

Public Member Functions
def	__init__ (self, dir)
def	switching_dynamics (self)
	loops over active contacts to determine if control authority is available or not
def	skew (self, v)
	converts vector v to skew symmetric matrix
def	quaternion_to_rotation (self, q)
	converts quaternion to rotation matrix
def	exp_quaternion (self, w)
	converts angular velocity to quaternion
def	log_quaternion (self, q)
	lives on the tangent space of SO(3)
def	quaternion_product (self, q1, q2)
	computes quaternion product of q1 x q2
def	integrate_quaternion (self, q, w)
	updates quaternion with tangent vector w
def	quaternion_difference (self, q1, q2)
	computes the tangent vector from q1 to q2 at Identity returns vecotr w s.t. More...
def	integrate_veocity (self, v, f)
def	integrate_angular_velocity (self, w, q, tau)
def	compute_trajectory_from_controls (self, x, u)
	xu0 contains initial trajectory at x[0], and controls for the full horizon
def	integrate_step (self, t, x, u)
	state vector x is given by x = [c, v, q, w] where c center of mass cartesian position v center of mass linear velocity q base orientation represented as a quaternion w base angular velocity
def	increment_x (self, x, dx)
	perturbs x with dx
def	diff_x (self, x1, x2)
	return the difference between x2 and x1 as x2 (-) x1 on the manifold
def	dynamics_derivatives (self, t, x, u)
	computes df/dx and df/du using finite differentiation
def	cost (self, t, x, u)
	a tracking cost for state and controls here we assume x0 to be the reference trajectory
def	cost_derivatives (self, t, x, u)
	compute cx, cxx, cu, cuu, cxu using finite differences
def	cost_dxdx (self, t, x, u)
def	cost_dudu (self, t, x, u)
	for quadratic tracking cost, structure is trivial uncomment finite difference for different cost implementation
def	cost_dxdu (self, t, x, u)
	structure is trivial for quadratic cost uncomment finite differences for any other structure
def	compute_Q (self, V_next, Vx_next, Vxx_next, t, x, u)
def	compute_value_function (self, t)
def	compute_gains (self)
	performs a backward pass to compute the lqr gain for the reference trajectories

Public Attributes
	dir
	com_pos
	com_vel
	com_ori
	com_ang_vel
	cent_force
	cent_moments
	contact_plan
	eps
	dt
	mass
	base_mass
	inertia_com_frame
	inertia_com_frame_scaled
	weight
	N
	n
	m
	nx
	active_contacts
	xp
	u0
	x0
	Q
	R
	value
	value_dx
	value_dxdx
	Q0
	Qdx
	Qdu
	Qdxdx
	Qdudu
	Qdxdu
	kfb
	kff

Static Private Member Functions
def	_smooth_inv (m)
	adds positive value to eigen values before inverting

Member Function Documentation

def momentumopt.kinoptpy.lqr_gain_manifold.CentroidalLqr.quaternion_difference	(		self,
			q1,
			q2
	)

computes the tangent vector from q1 to q2 at Identity returns vecotr w s.t.

q2 = exp(.5 * w)*q1

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The documentation for this class was generated from the following file:

• python/momentumopt/kinoptpy/lqr_gain_manifold.py