Tham khảo tài liệu 'humanoid robots part 16', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 368 Humanoid Robots where v t is the controller s output to the pitching or rolling joints us is the sensory input N is the order of controller. In this research framework we limit N 2 as it reduces the controller to two coupled neurons Zaier Nagashima 2006 . The parameters an 0 aj and bi can be easily designed since optimal values are not required in the proposed design approach. Therefore the motors commands can be expressed as follows z t v t ơ i t hi t 6 where hi t represents the reflex motion and zi t is the motor commands. Note that the solution of 3 is Sị t Siữ t 1 fi s 3ị ds and since gi t is a piecewise continuous in t and satisfies the Lipschitz condition over the interval t0 t1 time interval Os COM ---- Axis passing by COM Axis passing by equilibrium points x at tk CoM A switching mg ị at tk l Fig. 2. Commutation of the robot state between equilibrium points defined at the single support phase during commutation between single support phases then fi t 0i satisfies a local Lipschitz condition over the interval t0 t1 and has a unique solution Khalil 1996 . 3. Generation of walking motion pattern Stability at the single support phase While the inverted pendulum model considerably simplifies the control of the humanoid robot the inertia effect of distributed masses such as the arms may present a limitation to that approach. Our method although inspired by the inverted pendulum it considers not strictly the system dynamics. In other words the method can generate a rhythmic movement without solving the nonlinear differential equations of the system dynamics. To illustrate the idea consider where continuous commutations between single support phases take place. Let s model the system by a second order ODE with a feedback control input as follows New Approach of Neural Network for Controlling Locomotion and Reflex of Humanoid Robot 369 d2 a da 2f7 - a 7 where aDR is the counter clockwise angle of the inverted pendulum from the vertical Z DR is damping
