Central Pattern Generators for locomotion control in animals and robots: a review Ijspeert 2008

This is a very recent review of CPGs, from the bio to the robotics, just like it says. it is great. lots of ideas here. It also makes CPGs palatable. they are only called that out of inertia. Pretty much every below quote is assocaited with citations in the paper, even if i didn't list them.

CPGs are "Neural circuits capable of producing coordinated patterns of high dimensional rhythmic output signals while receving only simple low dimensional input signals"

CPGs "Implemented as neural networks or systems of coupled oscillators"

it doesn't seem that central pattern generators are so central. i expect they used to be, probably a grandmother cell, but now they are only central insofar as they exhibit course scale behavior. "central indicates that sensory feedback (from the peripheral nervous system) in not needed for generatig the rhythms...They present several intersting properties including distributed control, the ability to deal with redundancies, fast control loops, and sllowing modulation of locomotion by simple control sgnals"

"Also interesting collections of articles on biologically inspired robot locomotion can be found in Ayers, Davis, and Rudolph (2002), Beer, Chiel, Quinn, and Ritzmann (1998), Beer, Ritzmann, and McKenna (1993) And Kimura, Tsuchiya, Ishiguro, and Witte (2005)."

"..as reviewed by Delcomyn (1980)..." RE: CPGs Did i read that?

original debate about CPGs (and in general, the sensory vs central control of locomotion) goes back to 1911 C.S. Sherrington v.s. T.G.Brown.

fictive locomotion that is what you call it when a cat still walks after having its spine severed. I work on computers.

"Similar experiments have also shown that CPGs are distributed netowks made of multiple coupled oscillatory centers. Lamprey..."..."...While sensory feedback is not needed for generating the shythms, it plays a very important role in shaping the rhythmic patterns."

"..many reflexes are phase dependant, i.e. they have different effects depending on the timing within a locomotor cycle...see Rosignol et al. (2006) for an in-depth review of the interaction of CPGs and senesory feedback mechanisms."

"Interestingly, MLR stimulation also induces authomatic gait transition: in a decerebrated cat, increasing the stimulation leads to switched from walk to trot to gallop"

"Such a distributed organization presents several interesting features: (i) It reduces time delays in the motor control loop (rhythems are coordicated with mechanical movements using short feedback loops through the spical cord). (i) It dramatically reduces the dimensionality of the descending control signals. Indeed the control signals in general do no need to specify muscle activity but only modulate CPG activity. (iii) It therefore signiticatly reduces the necessary bacdwidth between the higher-level centers and the spinal cord."

"Oscillator models are based on mathematical models of coupled nonlinear oscillators to study population dynamics (Cohen, Holmes, &Rand, 1982; C ollins & Richmond, 1994; Ijspeert, Crespi, Ryczko, &Cabelguen, 2007; Kepell, Ermentrout, &Williams, 1991; Matsuoka, 1987; Schoner, Jian,&Kelso, 1990)."

"The motivation for this type of modeling comes from the fact that the dynamics of populations of oscillatory centers depend mainly on the type and topology of couplings rather than on the local mechanisms of rhythm generation, something that is well established in dynamical systems theory (Golubitsky & Stewart, 2002; Kuramoto, 2003)."

"sensory feedback that modulates CPG activity tends to lead to the most stable locomotion in complex terrain (as opposed to feedback that is independent of the CPG activity)" Fukuoka, Kimura & Cohen, 2003; Kimura et al,. 1999; Kimura, Fukuoka, & Cohen 2007)

" I identified at least five intersting propertis:

• (i)The pupose of CP models is to exhibit limit cycle behavior, i.i. to produce stable shythmic patterns. When this is the case, the system rapidly returns to its normal rhythmic behacior after transient perturnbations of the state variable...
• (ii) CPGs are well suited for distrbuted implementation, whic might be interesting for modular robots...
• (iii)CPG models typically have a few control parameteres that allow modulation of the locomotion, for instance the speed and direction or even the type of gait. A properly implemented CPG model therefore dreduces the deimenstionaity of the control problem such that higher-level controllers (or learning algorithms) do not need to drectly produce multidimensional motor commends but only higher-level control signals. ...
• (iv) CPGs are ideally suited to integrate sensory feedback signals (which can be added as coupling terms in the dirrerential aquations). This provieds the opportunity to obatin mutual entrainment between the CPG and the mechaical body...
• (v) CPG models usually offer a good substrate for learning and aptimization algorithms.

"

"This is related tot he fact that a sound methology does not exist yet for learning arbitrary limit cycles in dynamical systems, see a sidcussion in Buchli et al. (2006)."

"When constructing a CPG one has to deine the following idtems:

1. The genreal architecture of the CPG, This includes to thpe and numbe of oscillators or neruons.
2. The type and topogy of couplings. These willd etermine the conditions for synchornication between oscillators and the resulting gaits, i.e. the stalbe pase relations between oscillators.
3. The waveforms. These will determine what trajectories will actually be performed by each joint andle during a cycle. The waveforms are clearly dependent on the shape fo the limit cycle produced by the chosen (nerual) oscillator, but can be transorrmed by the addition of filters.
4. The effect of imnput signals, i.e. how control parameters can modulate important quantities such as the freuency, amplitude, phase lages, or wafeforms
5. The effect of feedback signals, i.e. how feedback from the body will affect tha activity of the CPG (for instance accelerating or decelerating it depending on environmental conditions).

A major difficulty in disgining CPGs is that the five design axes are all strongly interconnected.

The theory of dynamical systems can help in disigning CPGs. For ijstance, the theoyr can help in identifying when synchronication occues in a system of coupled oscillators depending of parameters such as couplinge ithgy and intricisc frequenceis... In particular it cn determince which pase diffeences are stable and unstable and this knowledge can be used to deisign systems of coupled oscillators that evolvee toward specific phase locked regimes...symmetry...Golubitsky..."

"We also explored the notion of programmable sCPGs that use pools of frequency adaptive oscillators to learn a specigic syhthmic pattern (Righetti & Ijspeert, 2005). An interesting aspect here is that learning is embedded into the dynamical systems..."

"Interestingly it seems that morphologies of vertebrates have chaged more than the underlying motor control circuits"

"Most robots have several resonant frequencies due to pendulum and/or mass-spring phenomena. It is typically useful to adapt gaits to these frequencies such as to minimuze energy sonsumption"

"Finally, one of the most imprtant open research topics the the development of a solid methodogy and theoritcal foundation for designing CPGs. Exellent theoritcal approaches have been developed for analyzing systems of couppled oscillators (Ermentrout & Kopell, 1991; Colubitsky & Stewear, 2002; Kopoell, 1995; Pham & Slotine, 2007; Pikovsky et al., 2001; Slotine & Li, 1991; Wang & Slotine, 2005), but many of these tools are not yet sufficent to completely deisng CPGs for a particular task, namely the fice design items listed [above]"

Problems

"A sound design methodology is missing for designing CPGs to solve a particluar locomotor problem... A second related challenge is that a solid theortical foundcation for describing CPGs is yet missing. For instance, it is very difficult to prove the stability of the complete CPG-robot system."