Considerations on dynamic and static stability of a biped robot

This paper describes the control of a biped robot, that uses an inverted pendulum for its balance. A control method that consists of the balance of the gaits, through the correction of the lateral and longitudinal angles of the pendulum is proposed in this work. This method presents three phases: first the trajectory of the foot in movement is defined, applying the inverse kinematics to calculate the robot's internal angles, and the direct kinematics is used to obtain the positions and orientations of the robot's joints; then the linear and angular accelerations are obtained; last, the zero moment point (ZMP) is calculated as a verification parameter of the requested margin of stability. Simulation of the robot gaits to walk in horizontal, sloping plans, and up and down stairs is also made. In order to decrease the calculation time of the dynamic stability, the impact of using zero pendulum angles as starting points for the interactive process of achieving the desired stability is compared to the use of the starting angles given by the static model. We also made a study to evaluate the necessary number of notable points to represent the gait to walk in horizontal plans. That evaluation demands to settle down a commitment between the stability quality and the computer effort, being therefore necessary to find a number of notable points that allows to reach that commitment, representing the gait satisfactorily.

[1]  Li Jun.  Biped Robot Walking Using Gravity-compensated Inverted Pendulum Mode , 2006 .

[2]  Y. Z. Li,et al.  Trajectory synthesis and physical admissibility for a biped robot during the single-support phase , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[3]  Carlos Canudas-de-Wit,et al.  Generation of energy optimal complete gait cycles for biped robots , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[4]  T. Takenaka,et al.  The development of Honda humanoid robot , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[5]  Christine Chevallereau,et al.  Low energy cost reference trajectories for a biped robot , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[6]  Tad McGeer,et al.  Passive walking with knees , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[7]  Jong H. Park,et al.  Biped robot walking using gravity-compensated inverted pendulum mode and computed torque control , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[8]  Miomir Vukobratović,et al.  Biped Locomotion: Dynamics, Stability, Control and Application , 1990 .

[9]  M. Vukobratovic,et al.  Biped Locomotion , 1990 .

[10]  M. Vukobratovic,et al.  Contribution to the Synthesis of Biped Gait , 1968 .

[11]  C. W. Radcliffe,et al.  Computer generation of human gait kinematics. , 1979, Journal of biomechanics.

[12]  Yuan F. Zheng,et al.  Gait synthesis for the SD-2 biped robot to climb sloping surface , 1990, IEEE Trans. Robotics Autom..

[13]  Kazuhito Yokoi,et al.  A high stability, smooth walking pattern for a biped robot , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[14]  Guy Bessonnet,et al.  Impactless sagittal gait of a biped robot during the single support phase , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).