Universally manipulable body models—dual quaternion representations in layered and dynamic MMCs

Abstract

Surprisingly complex tasks can be solved using a behaviour-based, reactive control system, i.e., a system that operates without an explicit internal representation of the environment and the own body. Nevertheless, application of internal representations has gained interest in recent years because such internal representations can be used to solve problems of perception and motor control (sensor fusion, inverse modeling) and may in addition be applied to higher cognitive functions as are the ability to plan ahead. To endow such a system with the ability to find new behavioural solutions to a given problem in a broad range of possibilities, the internal representation must be universally manipulable, i.e. the model should be able to simulate all movements that are physically possible for the body given. Using recurrent neural networks, models showing this faculty have been proposed being based on the principle of mean of multiple computation (MMC). The extension of this approach to three dimensions requires the introduction of a joint angle representation which allows for computation of mean values. Here we use dual quaternions that are singularity-free and unambiguous which allow for shortest path interpolation. In addition, it has been shown that dual quaternions are the most efficient and most compact form for representing rigid transformations. The model can easily be adapted to bodies of

Population based Mean of Multiple Computations networks: A building block for kinematic models

“…Mean of Multiple Computations (MMC) is a principle by which an RNN can be constructed to solve forward, inverse and mixed kinematic problems within one single model [5], [8], [14]. This is achieved by shaping the models attractor space to represent valid combinations of joint-configurations and end-effector positions.…”

“…This way, the network's attractor space is shaped to correctly represent kinematic constraints of the manipulator. As one additional connection in the recurrent neural network a form of self excitation is introduced which dampens the dynamics of the model and prevents oscillations [8]. The resulting network can be used to iteratively find configurations for all of the model's variables, if a subset of its variables is fixed to certain target values.…”

“…Sensor failures could be detected and accounted for, similar to the error-handling that's described in [19]. Again, as an additional influence and to stabilize the dynamics, comparable to the classical MMC approach [8], the current activation of a neuron is also fed back as an input to that neuron and is fused with the outputs of the MLPs. In that particular case a damping value is used to weight the different inputs (it describes the fraction of the input which is given through self excitation).…”

“…This method has proven to be quite flexible as it allows to solve inverse [6], forward or any mixed kinematic problem [7]. The principle has been applied to different kinds of representations in the past [8], [9], but in each case the single neurons of the networks directly encoded the represented values as activations. In the traditional MMC example, a segment position is encoded as a vector in two neurons.…”

A hexapod walker using a heterarchical architecture for action selection

“…According to this structure, only local decisions are required, which concern the decision between swing and stance for a given leg. Walknet has been expanded by a body model, briefly reviewed in Section Body Model (for details see Schilling, 2011; Schilling et al, 2012), that represents the kinematics of the body, i.e., all 18 joints of the six legs plus two body joints, each with 2° of freedom, as can be found in stick insects and as they are used by the physical hexapod robot Hector (Schneider et al, 2011). However, to allow for controlling different behaviors, further decision structures are required.…”