A holistic model for an internal representation to control the movement of a manipulator with redundant degrees of freedom

Abstract

The paper proposes a model for the control of a multisegmented manipulator with redundant degrees of freedom. On the basis of an earlier model, the socalled MMC net, a simpli®ed version is proposed here which has several advantages. First, it can easily be scaled up for the 3D case. Second, for the linear version a complete convergence proof is possible. Third, an easy way of implementing a damping parameter is shown. Fourth, the properties of the earlier model are unchanged, namely versatile control of the redundant system, immediate change from direct kinematics to inverse kinematics or any mixed control task, as well as robustness in the case of singularities.

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

“…In the classical MMC approach, additional external constraints have been introduced that counteract the segmentlength change. While the convergence of the model is guaranteed for the linear MMC model (Steinkühler and Cruse 1998), i.e., a model without external constraints acting on some variables, this has not be proven in general for the model extended through constraints which act in a nonlinear way on the variables. Until now there are only proofs for special cases (Steinkühler 1994).…”

“…While this network, termed mean of multiple computation (MMC) network, can be used as a forward model, as an inverse model and as any mixed model (Cruse and Steinkühler 1993;Steinkühler and Cruse 1998), it was originally applied only to 2D structures and the extension to 3D structures was restricted to Cartesian coordinates. An extension to general coordinates including joint angles, for example, requires additional processing of constraints which introduce non-linearities.…”

“…The classical MMC network (Cruse and Steinkühler 1993;Steinkühler and Cruse 1998) is an autoassociator, a type of self-organising map that is constrained by geometric relationships representing the kinematics of, to take a simple example, a serial chain manipulator, or, as a more complex case, of a six-legged walker with 18 degrees of freedom. By means of the geometric constraints, the network is forced into its attractor states, which always represent valid, geometrically correct solutions.…”

“…In the simplest case, the diagonal of the weight matrix consists of zeros. To prevent oscillations it has shown to be sufficient to introduce a damping factor d in the diagonal of the weight matrix (discussed in the Appendix of Steinkühler and Cruse 1998). The damping values can be related to the time constant of a low-pass filter (Makarov et al 2008).…”

Modelling memory functions with recurrent neural networks consisting of input compensation units: I. Static situations

“…In some contrast to these motor primitives, the situation models proposed here are not separable in forward models and inverse models, but each situation model combines both aspects in one holistic model (see also Cruse 2003). The units of these RNN models -like those of the somewhat more complex MMC nets (Steinkühler and Cruse 1998) -may be interpreted as showing properties of mirror neurons, or canonical neurons (Gallese and Lakoff 2005), because no functional separation is possible between neurons being related to perceptual or to motor tasks. These units correspond to what Gallese and Lakoff (2005) termed "multimodal neurons".…”