uaibot.utils module

class uaibot.utils.Utils

Bases: object

A library that contains some utilities for UAIbot. All of the functions are static.

IS_GROUPABLE = [‘uaibot.Ball’, ‘uaibot.Box’, ‘uaibot.SmoothBox’, ‘uaibot.Cylinder’, ‘uaibot.Frame’, ‘uaibot.RigidObject’, ‘uaibot.Group’, ‘uaibot.Robot’, ‘uaibot.PointLight’, ‘uaibot.Cone’]

IS_OBJ_SIM = [‘uaibot.Ball’, ‘uaibot.Box’, ‘uaibot.SmoothBox’, ‘uaibot.Cylinder’, ‘uaibot.Cone’, ‘uaibot.Robot’, ‘uaibot.PointLight’, ‘uaibot.Frame’, ‘uaibot.PointCloud’, ‘uaibot.Vector’, ‘uaibot.RigidObject’, ‘uaibot.Group’, ‘uaibot.HTMLDiv’]

IS_SIMPLE = [‘uaibot.Ball’, ‘uaibot.Box’, ‘uaibot.Cylinder’, ‘uaibot.SmoothBox’, ‘uaibot.Cone’]

static S(v)

Returns a 3x3 matrix that implements the cross product for a 3D vector
as a matricial product, that is, a matrix S(v) such that for any other 3D column vector w, S(v)w = cross(v,w).

Parameters

v: The vector for which the S matrix will be created.

Returns

S: A matrix that implements the cross product with v.

UAIBOT_NAME_TYPES = [‘uaibot.’, ‘cylinder.’, ‘box.’, ‘smoothbox.’, ‘ball.’, ‘robot.’, ‘simulation.’, ‘meshmaterial.’, ‘texture.’, ‘pointlight.’, ‘frame.’, ‘model3d.’, ‘links.’, ‘pointcloud.’, ‘vector.’, ‘rigidobject.’, ‘.group’, ‘.htmldiv’]

static axis_angle(htm)

Given an homogeneous transformation matrix representing a rotation, return the rotation axis angle.

Parameters

htm: 4X4 numpy array or nested list: Homogeneous transformation matrix of the rotation.

Returns

axis: The rotation axis.
angle: The rotation angle, in radians.

static bissection(fun, t0, tf, eps)

static compute_aabbdist(obj1, obj2)

static compute_dist(obj_a, obj_b, p_a_init=None, tol=0.001, no_iter_max=20)

static cubicsolve(p, lam)

static dp_inv(mat, eps=0.001)

Compute the damped pseudoinverse of the matrix ‘mat’.

Parameters

mat: nxm numpy array: The matrix to compute the damped pseudoinverse.
eps: positive float: The damping factor. (default: 0.001).

Returns

pinvA: mxn numpy array: The damped pseudoinverse of ‘mat’.

static euler_angles(htm)

Computer the Euler angles of a rotation matrix. Find alpha, beta and gamma such that.

htm = Utils.rotz(alpha) * Utils.roty(beta) * Utils.rotx(gamma).

Parameters

htm: 4X4 numpy array or nested list: Homogeneous transformation matrix of the rotation.

Returns

alpha: Rotation in z, in radians.
beta: Rotation in y, in radians.
gamma: Rotation in x, in radians.

static fun_Cir(v, h, r)

static fun_Int(v, h, L)

static fun_Sph(v, h, r)

static generate_connectivity_info(mesh_triangle, h)

static get_data_from_model(path)

static get_uaibot_type(obj)

Return the UAIBot type of the object. Return the empty string if it is not an UAIBot object.

Parameters

obj: object: Object to be verified.

Returns

obj_type: string: UAIBot type.

static hierarchical_solve(mat_a, mat_b, eps=0.001)

Solve the lexicographical unconstrained quadratic optimization problem

lexmin_x

mat_a[i]*x - b[i]

² + eps*

with lower indexes having higher priority than higher indexes.

Parameters

mat_a: A list of matrices (double arrays or numpy matrices).: The matrices mat_a[i]. All must have the same number of columns.
mat_b: A list of column vectors (double arrays or numpy matrices).: The vectors mat_b[i]. The number of rows of mat_b[i] must be equal to the number of rows of mat_a[i].
eps: positive float: Damping parameter. (default: 0.001).

Returns

x: numpy column vector: The solution x. For positive eps, the solution is always unique.

static htm_rand(trn=1, rot=1.5707963267948966)

Returns a random homogeneous transformation matrix.

Parameters

trn: float: Maximum parameter for random translation in x, y and z. (default: 1)
rot: float: Maximum parameter for random rotation in x, y and z. (default: 1)

Returns

htm: A homogeneous transformation matrix.

static interpolate(points)

Create a function handle that generates an one-time differentiable interpolated data from ‘points’.

The simplest case in when ‘points’ is a list with m elements. In this case, it will output a function f. When this function is evaluated at a scalar t, it will coincide with points[i] when t = i/m, that is, f(i/m) = points[i]. This function is once differentiable and periodic with period 1, so f(t+k)=f(t) for an integer k.

The function can also use a n x m numpy array or lists as ‘points’. In this case, f(t) is a n dimensional column vector in which its i-th entry is the same as computing f_i = interpolate(points[i]) and then computing f_i(t).

Finally, t can be a list of k elements instead of just a scalar. In this case, f(t) is a n x k numpy matrix in which the element at row i and column j is the same as computing f_i = interpolate(points[i]) and then computing f_i(t[k]).

Parameters

points: a n x m numpy array or lists: Points to be interpolated.

Returns

f: function handle: The function handle that implements the interpolation.

static inv_htm(htm)

Given a homogeneous transformation matrix, compute its inverse. It is faster than using numpy.linalg.inv in the case of HTMs.

Parameters

htm: 4X4 numpy array or nested list: Homogeneous transformation matrix of the rotation.

Returns

inv_htm: 4X4 numpy array: The inverse of the transformation matrix.

static is_a_color(obj)

Check if the argument is a HTML-compatible string that represents a color.

Parameters

obj: object: Object to be verified.

Returns

is_type: boolean: If the object is of the type.

static is_a_groupable_object(obj)

Check if the argument is a groupable object. Check the constant ‘Utils.IS_GROUPABLE’ for a list of groupable objects.

Parameters

obj: object: Object to be verified.

Returns

is_type: boolean: If the object is of the type.

static is_a_matrix(obj, n=None, m=None)

Check if the argument is a nxm matrix of floats.

Parameters

obj: object: Object to be verified.
n: positive int: Number of rows (default: it does not matter).
m: positive int: Number of columns (default: it does not matter).

Returns

is_type: boolean: If the object is of the type.

static is_a_name(string)

Check if the argument is a valid name for uaibot objects. Only characters [a-z], [A-z], [0-9] and ‘_’ are allowed. However, variables should not begin with numbers.

Parameters

string: string: Name to be verified.

Returns

is_name: boolean: If the name is a valid name.

static is_a_natural_number(obj)

Check if the argument is a natural number (integer and >=0)

Parameters

obj: object: Object to be verified.

Returns

is_type: boolean: If the object is of the type.

static is_a_number(obj)

Check if the argument is a float or int number

Parameters

obj: object: Object to be verified.

Returns

is_type: boolean: If the object is of the type.

static is_a_obj_sim(obj)

Check if the argument is an object that can be put into the simulator. Check the constant ‘Utils.IS_OBJ_SIM’ for a list of objects that can be put in the simulator.

Parameters

obj: object: Object to be verified.

Returns

is_type: boolean: If the object is of the type.

static is_a_pd_matrix(obj, n=None)

Check if the argument is a symmetric nxn positive (semi)-definite matrix.

Parameters

obj: object: Object to be verified.
n: positive int: Dimension of the square matrix (default: it does not matter).

Returns

is_type: boolean: If the object is of the type.

static is_a_simple_object(obj)

Check if the argument is a simple object. Check the constant ‘Utils.IS_SIMPLE’ for a list of simple objects.

Parameters

obj: object: Object to be verified.

Returns

is_type: boolean: If the object is of the type.

static is_a_vector(obj, n=None)

Check if the argument is a n vector of floats.

Parameters

obj: object: Object to be verified.
n: positive int: Number of elements (default: it does not matter).

Returns

is_type: boolean: If the object is of the type.

static is_url_available(url, types)

Try to access the content of the url ‘url’. Also verifies if the content is one of the extensions contained in ‘types’ (e.g, types = [‘png’, ‘bmp’, ‘jpg’, ‘jpeg’] for images).

Never throws an Exception, always returning a string with a message. Returns ‘ok!’ if and only if the url was succesfully acessed and has the correct file type.

Parameters

url: string: The url string.
types: list of string: The desired content extensions.

Returns

message: string: Message.

static jac(f, x, delta=0.0001)

Compute the numerical Jacobian of a function f at the point x. Uses centralized finite difference to compute the derivatives.

Parameters

f: function handle: The function handle. It should accept a single ‘m’ dimensional numpy array/matrix which is a column matrix and return a single ‘n’ dimensional numpy/array/matrix which is a column matrix.
x: m dimensional numpy columsn array/matrix: Point in which the Jacobian will be computed. This object should be of the same nature of the input of f, so f(x) is well-defined.
delta: float: Variation used in the numerical differentiation (default: 0.0001)

Returns

jac: n x m numpy array: The numerical Jacobian of f at point x. It is a n x m numpy array. If f_i(x) is the i-th entry of f(x) (1<=i<=n) and x_j the j-th variable (1<=j<=m), then the entry in the i-th row and j-th column is partial f_i/partial x_j evaluated at x.

static plot(xv, yv, title=’’, xname=’x’, yname=’y’, labels=’’)

static rot(axis, angle)

Homogeneous transformation matrix that represents the rotation of an angle in an axis.

Parameters

axis: The axis of rotation.
angle: float: The angle of rotation, in radians.

Returns

htm: The homogeneous transformation matrix.

static rotx(angle)

Homogeneous transformation matrix that represents the rotation of an angle in the ‘x’ axis.

Parameters

angle: float: The angle of rotation, in radians.

Returns

htm: The homogeneous transformation matrix.

static roty(angle)

Homogeneous transformation matrix that represents the rotation of an angle in the ‘y’ axis.

Parameters

angle: float: The angle of rotation, in radians.

Returns

htm: The homogeneous transformation matrix.

static rotz(angle)

Homogeneous transformation matrix that represents the rotation of an angle in the ‘z’ axis.