lambdas.py

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#
# Copyright (c) 2016 CNRS
#
 
import numpy as np
from pinocchio import Motion, Force, skew
from pinocchio.utils import zero
 
 
def jFromIdx(idxv, robot):
    """Return the joint index from the velocity index"""
    for j in range(1, robot.model.njoint):
        if idxv in range(
            robot.model.joints[j].idx_v,
            robot.model.joints[j].idx_v + robot.model.joints[j].nv,
        ):
            return j
 
 
parent = lambda i, robot: robot.model.parents[i]
iv = lambda i, robot: list(
    range(
        robot.model.joints[i].idx_v,
        robot.model.joints[i].idx_v + robot.model.joints[i].nv,
    )
)
ancestors = (
    lambda j, robot, res=[]: res
    if j == 0
    else ancestors(
        robot.model.parents[j],
        robot,
        [
            j,
        ]
        + res,
    )
)
 
 
class ancestorOf:
    def __init__(self, i, robot):
        self.dec = i
        self.robot = robot
 
    def __contains__(self, anc):
        dec = self.dec
        while dec > 0:
            if anc == dec:
                return True
            else:
                dec = self.robot.model.parents[dec]
 
 
# descendants = lambda root,robot: filter( lambda i: root in ancestorOf(i,robot), range(root,robot.model.njoints) )
descendants = lambda root, robot: robot.model.subtrees[root]
 
 
def setRobotArgs(robot):
    ancestors.__defaults__ = (robot,) + ancestors.__defaults__
    descendants.__defaults__ = (robot,)
    # ancestorsOf.__init__.__defaults__ = (robot,)
    iv.__defaults__ = (robot,)
    parent.__defaults__ = (robot,)
    jFromIdx.__defaults__ = (robot,)
 
 
# --- SE3 operators
Mcross = lambda x, y: Motion(x).cross(Motion(y)).vector
Mcross.__doc__ = "Motion cross product"
 
Fcross = lambda x, y: Motion(x).cross(Force(y)).vector
Fcross.__doc__ = "Force cross product"
 
MCross = lambda V, v: np.bmat([Mcross(V[:, i], v) for i in range(V.shape[1])])
FCross = lambda V, f: np.bmat([Fcross(V[:, i], f) for i in range(V.shape[1])])
 
 
adj = lambda nu: np.bmat([[skew(nu[3:]), skew(nu[:3])], [zero([3, 3]), skew(nu[3:])]])
adj.__doc__ = "Motion pre-cross product (ie adjoint, lie bracket operator)"
 
adjdual = lambda nu: np.bmat(
    [[skew(nu[3:]), zero([3, 3])], [skew(nu[:3]), skew(nu[3:])]]
)
adjdual.__doc__ = "Force pre-cross product adjdual(a) = -adj(a)' "
 
td = np.tensordot
quad = lambda H, v: np.array(td(td(H, v, [2, 0]), v, [1, 0]))
quad.__doc__ = """Tensor product v'*H*v, with H.shape = [ nop, nv, nv ]"""
 
 
def np_prettyprint(sarg="{: 0.5f}", eps=5e-7):
    mformat = (
        lambda x, sarg=sarg, eps=eps: sarg.format(x) if abs(x) > eps else " 0.     "
    )
    np.set_printoptions(formatter={"float": mformat})