Introducing a Cartesian approach for gate planning and control of biped robots and implementing on various slopes

Biped robots have higher capabilities than other mobile robots, for moving on uneven environments. However, due to natural instability of these robots, their motion planning and control become a more important and challenging task. This article, will present a Cartesian approach for gate planning and control of biped robots without needing to use the joint space trajectories and the inverse kinematics. The proposed approach is based on constraining four important points of the biped robot in Cartesian space. This leads to overcome the redundancy problem and use the concept of Transpose Jacobian control as a virtual spring and damper between each of these points and the corresponding desired trajectory. These four points include the tip of right and left foot, the hip joint and the total center of mass (CM). Furthermore, in the control of the biped robots based on desired trajectories in task space, the system may track the desired trajectory while the knee is broken. This problem is solved here using a PD controller which will be called the Knee Stopper. Similarly, another PD controller is proposed as the Trunk Stopper to limit the trunk motion. Obtained results show that the proposed Cartesian approach can be successfully used in tracking desired trajectories on various slopes.