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describe a simulated six-legged robot

legs swing about a single joint with the body

five neurons to control a single leg

describe the network architecture of the locomotion controller

50 (network weights)

how many parameters consist of a neural controller?

via binary string

how is the neural controller encoded?

what is the fitness function of a neural controller based on?

it's bsaed on the distance traveled in a fixed time period

the TRIPOD gait

what is the gait favored for fast walking?

via dynamical systems (no need to memorize equations)

how can we quantitatively evaluate the types of tripod walkers?

what the basic components of a dynamical system?

system, state, state space, state variables, trajectory, phase portrait, attractors, basin, repellors, saddle

define a system

a set of interacting factors (called state variables) whose values change over time (population of owls, mice, and availability of grain)

define a state

vector of values, one for each variable of the system at a given moment (20 owls, 30 mice, 1.5 lb of grain)

define a state space

all possible states of the system (# of owls, mice, amt of grain left)

define an instantaneous velocity vector

rate/direction of change in teh state of the system at a point in time

vector field

collection of all of the instantaneous velocity vectors--TECHNICALLY, a dynamical system is equivalent to this vector field

define a trajectory

cruve connecting temporally successive points in a state space

define a phase portrait

a state space filled with trajectories of a given model

the trajectories (phase portrait)

what gives the history of change of the system over time

describe a periodic trajectory

it is a cyclic, closed trajectory--it closes upon itself

describe a fixed point in a phase portrait

a point in the state space with zero instantaneous velocity (constant, critical, rest point)

desribe an attractor

limit sets to which all nearby trajectories tend towards--can be a fixed attractor, periodic, or chaotic

define a basin

region of the state space containing all trajectories which tend to a given attractor

define a repellor

points and periodic trajectories from which trajectories only leave

define a saddle

limit sets which some trajectories approach and others depart

define a chaotic trajectory

trajectories that are neither fixed nor cyclic but which fill up a constrained region of the state space (does not go to a fixed point or a cycle, but remains constrained in a region of phase space)

using a 2-neuron system

how can we produce such dynamical systems?

define a Lorenz attractor

used to study weather phenomena, and traces a single trajectory

define a strange attractor

all particles converge to a same volume

agent and its environment as coupled dynamical systems

how can we use dynamical systems to model robotics and evolution?

define the three classes of evolved controllers

if sensors were enabled during evolution, then reflexive pattern generators evolved

define the 5D projection of the pattern generators/evolved controllers

it's a 5D limit cycle, motor space projection, plots the output of foot, backward swing, forward swing

using the 5D projections; compare 3D curves

how can we compare behavior between evolved controllers?