Abstract
Synchronization of coupled non-linear oscillators inspired by a central pattern generator (CPG) can control the bionic robot and promote the coordination and diversity of locomotion. However, for a robot with a strong mutual coupled structure, such neurobiological control is still missing. In this contribution, we present a σ-Hopf harmonic oscillator with decoupled parameters to expand the solution space of the locomotion of the robot. Unlike the synchronization of original Hopf oscillators, which has been fully discussed, the asymmetric factor of σ-Hopf oscillator causes a deformation in oscillation waveform. Using the non-linear synchronization theory, we construct the transition state model of the synchronization process to analyze the asymmetrical distortion, period change and duty ratio inconsistency. Then a variable coupling strength is introduced to eliminate the waveform deformation and maintain the fast convergence rate. Finally, the approach is used for the locomotion control of a bionic parallel waist of legged robot, which is a highly coupled system. The effectiveness of the approach in both independent and synthesis behavior of four typical motion patterns are validated. The result proves the importance of controllability of the oscillation waveform and the instantaneous state of the synchronization, which benefits the transition and transformation of the locomotion and makes the coupling motion more flexible.
Highlights
Legged robot technique has made remarkable progress in the past few decades, and produced a series of very famous achievements: StarlETH (Hutter et al, 2012), ANYmal (Hutter et al, 2016; Hwangbo et al, 2019), HyQ series (Semini et al, 2011, 2016), MIT Cheetah series (Seok et al, 2013; Wensing et al, 2017), Boston Dynamics Spotmini series1
The bionic torso structure can be divided into two types: torso with active joint (Khoramshahi et al, 2013; Satoh and Fujimoto, 2018) and with passive joint (Takuma et al, 2010; Haynes et al, 2012)
The parallel structure has been directly applied to legged robot, showing better performance than serial structure (Kuehn et al, 2017), no bionical method is used on the parallel structure
Summary
Legged robot technique has made remarkable progress in the past few decades, and produced a series of very famous achievements: StarlETH (Hutter et al, 2012), ANYmal (Hutter et al, 2016; Hwangbo et al, 2019), HyQ series (Semini et al, 2011, 2016), MIT Cheetah series (Seok et al, 2013; Wensing et al, 2017), Boston Dynamics Spotmini series. These oscillator-based models can periodically generate nonlinear oscillation signals and are widely used as CPG oscillation units since they contain a fewer number of parameters and have sophisticated background implementation theories All of these above can be used for robot control and the networks with oscillators will not differ too much within the same robot, with respect to the architecture and coupling topology, which are related to the physical structure and control frame. This consideration has been fully discussed both in architectural symmetries and diffusion-like couplings (Buono and Golubitsky, 2001; Ashwin, 2003; Ramezani et al, 2017) Another point is that the transition process needs to be clear and controllable, since it concerns the trajectory of every movement of the limbs and joints. Synchronization of σ-Hopf oscillators for the bionic parallel waist of a legged robot is proposed to realize neurobiologically inspired control.
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