Researches related to legged robot has had impressive advances in the last several decades, from animal-like to walking humanoid robots. Development of biped robots that mimic the behavior of man-kind is indeed a formidable task. It's necessary for the robots to adopt its motion with different ground condition and maintain its stability with suitable motion of legs and trunk. In this thesis, dynamic modeling, dynamic stability and trajectory planning of a seven-link planar biped robot, walking on different circumstances, are studied. The biped robot consists of seven links, which represents trunk, thigh, shin and metatarsal. The links are attached together by six revolute joint.There is an actuator in each joint and all of the joints are only in the sagittal plane and friction less. Dynamic stability of biped robot walking is dependent on good path planning. Most researches of path planning generate hip and ankle joints trajectories because by knowing this trajectories walking path planning would be completed. Generation of smooth trajectories for ankle and hip joints in Cartesian space using polynomials with suitable order are designed such that the first and the second time derivatives are continuous all the time and impact effect of feet with ground is eliminated. In this thesis, a method of path generation for biped robot at different walking conditions and circumstances is proposed. A walking cycle with ability of changing the step length has been considered for path planning of Robot motion on sagittal plane on smooth horizontal surface. Each walking steps include two phases, single support phase and double support phase.By using this method, Robot is able to walk with step changes and different time steps. Having the kinematic constraints, trajectories of hip and ankle joints, are designed with two unknown coefficients hip which are to be determined to ensure dynamic stability. By gathering these coefficients in different walking conditions and for different robots, a training fuzzy system based on man experience is used to find these coefficients in new circumstances. Identification of fuzzy system parameters is based on gradient descent method and it is done for Takagi-Sugeno fuzzy system parameter adaption by using training data set. Zero moment point (ZMP) which was first introduced by Vukobratovic is used as the stability criterion.Also we use virtual ZMP on stair that is introduced based on virtual slope method. Proposed method also is applied for walking on slope and stairs. Finally, walking on smooth, up/down slope and stair is simulated. Simulation results show that the robot is able to walk stable in different circumstances. Keywords: Biped robot, zero moment point, fuzzy path generator, fuzzy system identification
