This paper presents modeling of a 12-degree of freedom （DoF） bipedal robot, focusing on the lower limbs of the system, and trajectory design for walking on straight path. Gait trajectories are designed by modeling o...This paper presents modeling of a 12-degree of freedom （DoF） bipedal robot, focusing on the lower limbs of the system, and trajectory design for walking on straight path. Gait trajectories are designed by modeling of center of mass （CoM） trajectory and swing foot ankle trajectory based on stance foot ankle. The dynamic equations of motion of the bipedal robot are derived by considering the system as a quasi inverted pendulmn （QIP） model. The direction and acceleration of CoM movement of the QIP model is determined by the position of CoM relative to the centre of pressure （COP）. To determine heel-contact and toe-off, two custom designed switches are attached with heel and toe positions of each foot. Four force sensitive resistor （FSR） sensors are also placed at the plantar surface to measure pressure that is induced on each foot while walking which leads to the calculation of CoP trajectory. The paper also describes forward kinematic （FIK） and inverse kinematic （IK） investigations of the biped model where Denavit-Hartenberg （D-H） representation and Geometric-Trigonometric （G-T） formulation approach are applied. Experiments are carried out to ensure the reliability of the proposed model where the links of the bipedal system follow the best possible trajectories while walking on straight path.展开更多
We present a systematic and efficient Chebyshev spectral method using quasiinverse technique to directly solve the second order equation with the homogeneous Robin boundary conditions and the fourth order equation wit...We present a systematic and efficient Chebyshev spectral method using quasiinverse technique to directly solve the second order equation with the homogeneous Robin boundary conditions and the fourth order equation with the first and second boundary conditions.The key to the efficiency of the method is to multiply quasiinverse matrix on both sides of discrete systems,which leads to band structure systems.We can obtain high order accuracy with less computational cost.For multi-dimensional and more complicated linear elliptic PDEs,the advantage of this methodology is obvious.Numerical results indicate that the spectral accuracy is achieved and the proposed method is very efficient for 2-D high order problems.展开更多
基金supported by Ministry of Higher Education,Malaysia through the MyRA Incentive Grant Scheme(No.MIRGS13-02-001-0001)
文摘This paper presents modeling of a 12-degree of freedom （DoF） bipedal robot, focusing on the lower limbs of the system, and trajectory design for walking on straight path. Gait trajectories are designed by modeling of center of mass （CoM） trajectory and swing foot ankle trajectory based on stance foot ankle. The dynamic equations of motion of the bipedal robot are derived by considering the system as a quasi inverted pendulmn （QIP） model. The direction and acceleration of CoM movement of the QIP model is determined by the position of CoM relative to the centre of pressure （COP）. To determine heel-contact and toe-off, two custom designed switches are attached with heel and toe positions of each foot. Four force sensitive resistor （FSR） sensors are also placed at the plantar surface to measure pressure that is induced on each foot while walking which leads to the calculation of CoP trajectory. The paper also describes forward kinematic （FIK） and inverse kinematic （IK） investigations of the biped model where Denavit-Hartenberg （D-H） representation and Geometric-Trigonometric （G-T） formulation approach are applied. Experiments are carried out to ensure the reliability of the proposed model where the links of the bipedal system follow the best possible trajectories while walking on straight path.
基金supported by the grants of National Natural Science Foundation of China(No.10731060,10801120)Chinese Universities Scientific Fund No.2010QNA3019.
文摘We present a systematic and efficient Chebyshev spectral method using quasiinverse technique to directly solve the second order equation with the homogeneous Robin boundary conditions and the fourth order equation with the first and second boundary conditions.The key to the efficiency of the method is to multiply quasiinverse matrix on both sides of discrete systems,which leads to band structure systems.We can obtain high order accuracy with less computational cost.For multi-dimensional and more complicated linear elliptic PDEs,the advantage of this methodology is obvious.Numerical results indicate that the spectral accuracy is achieved and the proposed method is very efficient for 2-D high order problems.
