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.

To find a common approach for the development of an efficient system that is able to achieve an omnidirectional jump, a jumping kinematic of a legged robot is proposed based on the behavior mechanism of a jumping spider. To satisfy the diversity of motion forms in robot jumping, a kind of 4 degrees of freedom (4DoFs) mechanical leg is designed. Taking the change of joint angle as inspiration by observing the behavior of the jumping spider during the acceleration phase, a redundant constraint to solve the kinematic is obtained. A series of experiments on three types of jumping—vertical jumping, sideways jumping and forward jumping—is carried out, while the initial attitude and path planning of the robot is studied. The proposed jumping kinematic is verified on the legged robot experimental platform, and the added redundant constraint could be verified as being reasonable. The results indicate that the jumping robot could maintain stability and complete the planned task of jumping, and the proposed spider-inspired jumping strategy could easily achieve an omnidirectional jump, thus enabling the robot to avoid obstacles.

Aimed at solving the misplaced body trajectory problem caused by the rolling of semi-round rigid feet when a robot is walking, a legged kinematic trajectory correction methodology based on the Least Squares Support Vector Machine (LS-SVM) is proposed. The concept of ideal foothold is put forward for the three-dimensional kinematic model modification of a robot leg, and the deviation value between the ideal foothold and real foothold is analyzed. The forward/inverse kinematic solutions between the ideal foothold and joint angular vectors are formulated and the problem of direct/inverse kinematic nonlinear mapping is solved by using the LS-SVM. Compared with the previous approximation method, this correction methodology has better accuracy and faster calculation speed with regards to inverse kinematics solutions. Experiments on a leg platform and a hexapod walking robot are conducted with multi-sensors for the analysis of foot tip trajectory, base joint vibration, contact force impact, direction deviation, and power consumption, respectively. The comparative analysis shows that the trajectory correction methodology can effectively correct the joint trajectory, thus eliminating the contact force influence of semi-round rigid feet, significantly improving the locomotion of the walking robot and reducing the total power consumption of the system.