Design methodologies for central pattern generators: An application to crawling humanoids

Systems of coupled nonlinear oscillators inspired from animal central pattern generators (CPGs) are increasingly used for the control of locomotion in robots, in particular for online trajectory generation. Indeed, such systems present interesting characteristics like limit cycle behavior (i.e. stability), synchronization, and the possibility to be entrained and modulated by external signals. There are now good methodologies for designing systems that exhibit specific gaits, i.e. specific phase relations between oscillators, however techniques to modulate the shape of the rhythmic signals in a controlled way are still missing. In this article, we present a method for shaping the signals of an oscillatory system according to several criteria that are relevant for locomotion control (but which could also be useful for other applications). These criteria include being able to adjust the relative durations of ascending and descending phases in a cycle, and to temporarily modulate the dynamics of one oscillator according to the states of another one. The first criterion is important for locomotion in order to adjust the duration of swing and stance phases, while the second allows one to introduce signal shape variations to deal with proper inter-limb coordination. We apply the method to the design of a system of coupled oscillators used to control crawling in a simulated humanoid robot. Using some key characteristics of signal shapes extracted from recordings of baby crawling, we design the system to produce stable trot-like crawling gaits. Insights from symmetry groups' theory are used to design the right phase lags. The oscillators are designed such that the speed of locomotion can be adjusted by varying the duration of the stance phase while keeping the duration of the swing phase constant, like in most tetrapod animals.