The spring-loaded inverted pendulum(SLIP) has been widely studied in both animals and robots.Generally,the majority of the relevant theoretical studies deal with elastic leg,the linear leg length-force relationship of...The spring-loaded inverted pendulum(SLIP) has been widely studied in both animals and robots.Generally,the majority of the relevant theoretical studies deal with elastic leg,the linear leg length-force relationship of which is obviously conflict with the biological observations.A planar spring-mass model with a nonlinear spring leg is presented to explore the intrinsic mechanism of legged locomotion with elastic component.The leg model is formulated via decoupling the stiffness coefficient and exponent of the leg compression in order that the unified stiffness can be scaled as convex,concave as well as linear profile.The apex return map of the SLIP runner is established to investigate dynamical behavior of the fixed point.The basin of attraction and Floquet Multiplier are introduced to evaluate the self-stability and initial state sensitivity of the SLIP model with different stiffness profiles.The numerical results show that larger stiffness exponent can increase top speed of stable running and also can enlarge the size of attraction domain of the fixed point.In addition,the parameter variation is conducted to detect the effect of parameter dependency,and demonstrates that on the fixed energy level and stiffness profile,the faster running speed with larger convergence rate of the stable fixed point under small local perturbation can be achieved via decreasing the angle of attack and increasing the stiffness coefficient.The perturbation recovery test is implemented to judge the ability of the model resisting large external disturbance.The result shows that the convex stiffness performs best in enhancing the robustness of SLIP runner negotiating irregular terrain.This research sheds light on the running performance of the SLIP runner with nonlinear leg spring from a theoretical perspective,and also guides the design and control of the bio-inspired legged robot.展开更多
As a well-explored template that captures the essential dynamical behaviors of legged locomotion on sagittal plane,the spring-loaded inverted pendulum(SLIP)model has been extensively employed in both biomechanical stu...As a well-explored template that captures the essential dynamical behaviors of legged locomotion on sagittal plane,the spring-loaded inverted pendulum(SLIP)model has been extensively employed in both biomechanical study and robotics research.Aiming at fully leveraging the merits of the SLIP model to generate the adaptive trajectories of the center of mass(CoM)with maneuverability,this study presents a novel two-layered sagittal SLIP-anchored(SSA)task space control for a monopode robot to deal with terrain irregularity.This work begins with an analytical investigation of sagittal SLIP dynamics by deriving an approximate solution with satisfactory apex prediction accuracy,and a two-layered SSA task space controller is subsequently developed for the monopode robot.The higher layer employs an analytical approximate representation of the sagittal SLIP model to form a deadbeat controller,which generates an adaptive reference trajectory for the CoM.The lower layer enforces the monopode robot to reproduce a generated CoM movement by using a task space controller to transfer the reference CoM commands into joint torques of the multi-degree of freedom monopode robot.Consequently,an adaptive hopping behavior is exhibited by the robot when traversing irregular terrain.Simulation results have demonstrated the effectiveness of the proposed method.展开更多
基金supported by National Natural Science Foundation of China(Grant No.61175107)National Hi-tech Research and Development Program of China(863 Program+3 种基金Grant No.2011AA0403837002)Self-Planned Task of State Key Laboratory of Robotics and SystemHarbin Institute of TechnologyChina(Grant No.SKLRS201006B)
文摘The spring-loaded inverted pendulum(SLIP) has been widely studied in both animals and robots.Generally,the majority of the relevant theoretical studies deal with elastic leg,the linear leg length-force relationship of which is obviously conflict with the biological observations.A planar spring-mass model with a nonlinear spring leg is presented to explore the intrinsic mechanism of legged locomotion with elastic component.The leg model is formulated via decoupling the stiffness coefficient and exponent of the leg compression in order that the unified stiffness can be scaled as convex,concave as well as linear profile.The apex return map of the SLIP runner is established to investigate dynamical behavior of the fixed point.The basin of attraction and Floquet Multiplier are introduced to evaluate the self-stability and initial state sensitivity of the SLIP model with different stiffness profiles.The numerical results show that larger stiffness exponent can increase top speed of stable running and also can enlarge the size of attraction domain of the fixed point.In addition,the parameter variation is conducted to detect the effect of parameter dependency,and demonstrates that on the fixed energy level and stiffness profile,the faster running speed with larger convergence rate of the stable fixed point under small local perturbation can be achieved via decreasing the angle of attack and increasing the stiffness coefficient.The perturbation recovery test is implemented to judge the ability of the model resisting large external disturbance.The result shows that the convex stiffness performs best in enhancing the robustness of SLIP runner negotiating irregular terrain.This research sheds light on the running performance of the SLIP runner with nonlinear leg spring from a theoretical perspective,and also guides the design and control of the bio-inspired legged robot.
基金This work was supported by the National Natural Science Foundation of China(Grant No.51605115)State Key Laboratory of Robotics and System(Self-Planned Task No.SKLRS201719A)+1 种基金Heilongjiang Postdoctoral Financial Assistance(Grant No.LBH-Z16083)Natural Science Foundation of Heilongjiang Province(Grant No.QC2017052).
文摘As a well-explored template that captures the essential dynamical behaviors of legged locomotion on sagittal plane,the spring-loaded inverted pendulum(SLIP)model has been extensively employed in both biomechanical study and robotics research.Aiming at fully leveraging the merits of the SLIP model to generate the adaptive trajectories of the center of mass(CoM)with maneuverability,this study presents a novel two-layered sagittal SLIP-anchored(SSA)task space control for a monopode robot to deal with terrain irregularity.This work begins with an analytical investigation of sagittal SLIP dynamics by deriving an approximate solution with satisfactory apex prediction accuracy,and a two-layered SSA task space controller is subsequently developed for the monopode robot.The higher layer employs an analytical approximate representation of the sagittal SLIP model to form a deadbeat controller,which generates an adaptive reference trajectory for the CoM.The lower layer enforces the monopode robot to reproduce a generated CoM movement by using a task space controller to transfer the reference CoM commands into joint torques of the multi-degree of freedom monopode robot.Consequently,an adaptive hopping behavior is exhibited by the robot when traversing irregular terrain.Simulation results have demonstrated the effectiveness of the proposed method.
