Table Of Contents
Table Of Contents

Organism #1

class sensorimotor_dependencies.organisms.Organism1(seed=1, retina_size=1.0, M_size=40, E_size=40, nb_joints=4, nb_eyes=2, nb_lights=3, extero=20, proprio=4, nb_generating_motor_commands=50, nb_generating_env_positions=50, neighborhood_size=1e-08, sigma=<ufunc 'tanh'>)[source]

Organism 1:

By default:

  1. The arm has

  • nb_joints joints

    • each of which has proprio proprioceptive sensors

    (whose outputs depend on the position of the joint)

  • nb_eyes eyes (for each of them: 3 spatial and 3 orientation coordinates)

    • on which there are extero omnidirectional exteroceptive photosensors

  1. the motor command is M_size-dimensional

  2. the environment consists of:

    • nb_lights lights (3 spatial coordinates and nb_lights luminance values for each of them)

Other parameters:

  • Random seed: seed
  • Sensory inputs are generated from nb_generating_motor_commands motor commands and nb_generating_env_positions environment positions
  • Neighborhood size of the linear approximation: neighborhood_size i.e. Motor commands/Environmental positions drawn from normal distribution with mean zero and standard deviation neighborhood_size (Coordinates differing from 0 by more than the std deviation are set equal to 0)
  • retina_size size of the retina: variance of the normal distribution from which are drawn the C[i,k] (relative position of photosensor k within eye i)
Parameter Value
Dimension of motor commands M_size
Dimension of environmental control vector E_size
Number of eyes nb_eyes
Number of joints nb_joints
Dimension of proprioceptive inputs proprio*nb_joints
Dimension of exteroceptive inputs extero*nb_eyes
Diaphragms None
Number of lights nb_lights
Light luminance Fixed
get_dimensions(dim_red='PCA', return_eigenvalues=False)[source]

Compute and returns the estimated dimension of the rigid group of compensated movements and the estimated number of parameters needed to describe the variations in the exteroceptive inputs when: only the body (resp. the environment, resp. both of them) change.

The procedure is the following one:

  1. One gets rid of proprioceptive inputs by noting that these don’t change when no motor command is issued and the environment changes, contrary to exteroceptive inputs.
  2. We estimate the dimension of the space of sensory inputs obtained through variations of the motor commands only with resort to a dimension reduction technique (utils.PCA or utils.MDS).
  3. We do the same for sensory inputs obtained through variations of the environment only.
  4. We reiterate for variations of both the *motor commands and the environment alike.
  5. Finally, we compute the dimension of the rigid space of compensated movements: it is the sum of the formers minus the latter.

At the end, the results

  • are stored in a markdown table string: self.dim_table
  • are added to the representation string (accessed via __str__) of the object
Parameters:
  • dim_red ({'PCA', 'MDA'}, optional) – Dimension reduction algorithm used to compute the number of degrees of freedom (PCA by default).
  • return_eigenvalues (bool, optional) – Returns the eigenvalues and their ratios \(λ_{i+1}/λ_i\) (False by default).
Returns:

self.dim_rigid_group, self.dim_extero, self.dim_env, self.dim_env_extero – Estimated dimension of the rigid group of compensated movements (stored in self.dim_rigid_group), and number of parameters needed to describe the exteroceptive variations when:

  1. only the body moves
  • this number is stored in self.dim_extero
  1. only the environment changes
  • this number is stored in self.dim_env
  1. both the body and the environment change
  • this number is stored in self.dim_env_extero
Return type:

tuple(int, int, int, int)

Examples

>>>  O = organisms.Organism1(); O.get_dimensions()
(4, 10, 5, 11)

>>> print(O.dim_table)
**Characteristics**|**Value**
-|-
Dimension for body (p)|10
Dimension for environment (e)|5
Dimension for both (b)|11
Dimension of group of compensated movements|4

>>> print(str(O))
**Characteristics**|**Value**
-|-
Dimension of motor commands|40
Dimension of environmental control vector|40
Dimension of proprioceptive inputs|16
Dimension of exteroceptive inputs|40
Number of eyes|2
Number of joints|4
Diaphragms|None
Number of lights|3
Light luminance|Fixed
Dimension for body (p)|10
Dimension for environment (e)|5
Dimension for both (b)|11
Dimension of group of compensated movements|4

>>> print(organisms.Organism1(extero=1).get_dimensions(return_eigenvalues=True))
(1, 1, 1, 1, [array([  5.28255070e-33,   1.23259516e-32]), array([  7.29495097e-33,   8.04960107e-33]), array([  7.26535685e-33,   7.52677159e-33])], [[2.333333333333333], [1.103448275862069], [1.035980991174474]])
get_proprioception(return_trials=False)[source]

Computes a mask indicating the sensory inputs the organism can reliably deem to be proprioceptive, since they remain silent when: - the motor command is fixed - the environment changes

Useful to separate proprioceptive inputs from exteroceptive ones

Examples

>>> O = organisms.Organism1(proprio=1, nb_joints=2, extero=1, nb_eyes=2); O.get_proprioception(); O.mask_proprio
array([ True,  True, False, False], dtype=bool)

>>> from sensorimotor_dependencies import organisms; O = organisms.Organism1(); O.get_proprioception(return_trials=True)
array([[-0.07403972, -0.27175696, -0.57920141, ...,  0.19565543,
        0.52651921,  0.43479947],
      [-0.07403972, -0.27175696, -0.57920141, ...,  0.19565542,
        0.52651921,  0.43479947],
      [-0.07403972, -0.27175696, -0.57920141, ...,  0.19565543,
        0.52651921,  0.43479947],
      ...,
      [-0.07403972, -0.27175696, -0.57920141, ...,  0.19565542,
        0.52651921,  0.43479947],
      [-0.07403972, -0.27175696, -0.57920141, ...,  0.19565542,
        0.52651921,  0.43479947],
      [-0.07403972, -0.27175696, -0.57920141, ...,  0.19565542,
        0.5265192 ,  0.43479947]])
get_sensory_inputs(M, E, QPaL=None)[source]

Compute sensory inputs for motor command M and environment position E

$$\begin{align*} (Q,P,a) &≝ σ(W_1 · σ(W_2 · M − μ_2)−μ_1\\ L &≝ σ(V_1 ·σ(V_2 · E − ν_2) − ν_1)\\ ∀1≤ k ≤ p’, 1≤i≤p, \quad S^e_{i,k} &≝ d_i \sum\limits_{j} \frac{θ_j}{\Vert P_i + Rot(a_i^θ, a_i^φ, a_i^ψ) \cdot C_{i,k} - L_j \Vert^2}\\ (S^p_i)_{1≤ i ≤ q’q} &≝ σ(U_1 · σ(U_2 · Q − τ_2) − τ_1)\\ \end{align*}$$

where

  • \(W_1, W_2, V_1, V_2, U_1, U_2\) are matrices with coefficients drawn randomly from a uniform distribution between \(−1\) and \(1\)
  • the vectors \(μ_1, μ_2, ν_1, ν_2, τ_1, τ_2\) too
  • \(σ\) is an arbitrary nonlinearity (e.g. the hyperbolic tangent function)
  • the \(C_{i,k}\) are drawn from a centered normal distribution

whose variance (which can be understood as the size of the retina) is so that the sensory changes resulting from a rotation of the eye are of the same order of magnitude as the ones resulting from a translation of the eye - \(θ\) and \(d\) are constants drawn at random in the interval \([0.5, 1]\)

Parameters:
  • M ((M_size,) array) – Motor command vector
  • E ((E_size,) array) – Environmental control vector
  • QPaL ({4-tuple of arrays, None}, optional) –

    \(Q, P, a\) and \(L\) values. If left unspecified, then they are computed as above, with the _get_QPaL method.

    This optional argument come in handy for Organisms 2 and 3, for which we use this very method (avoiding heavy overloading)
Returns:

Concatenation of proprioceptive and exteroceptive sensory inputs
Return type:

(proprio*nb_joints + extero*nb_eyes,) array
get_variations()[source]
Compute the variations in the exteroceptive inputs when:
  1. only the environment changes
  • result stored in self.env_variations
  1. only the motor commands change
  • result stored in self.mot_variations
  1. both change
  • result stored in self.env_mot_variations
neighborhood_lin_approx(size)[source]

Neighborhood linear approximation:

Parameters:size (int) – Neighborhood size of the linear approximation
Returns:rand_vect – Random vector drawn from a normal distribution with mean zero and standard deviation neighborhood_size where coordinates differing from 0 by more than the standard deviation have been set equal to 0
Return type:(size,) array
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Organism #2