Trajectory planning for smooth transition of a biped robot

interpolation based trajectory planning method which is aiming to achieve smooth biped swing leg trajectory by reducing the instant velocity change which occurs at the time of collision of the biped swing leg with the ground. We first characterize the bipedal walking cycle and point out some major issues that need to be addressed to plan a continuous swing leg trajectory by using the concept of the spline interpolation and zero moment points (ZMP). We demonstrate that the impact effects can be avoided at the time of the swing foot's heel touching with the ground. The proposed biped trajectory planning method has been tested on our soccer-playing humanoid robot, Robo-Erectus, which got Second Place at the 2002 RoboCup Humanoid Walk competition. Trajectory planning is crucial for a stable motion of biped robots [5, 10, 11]. In particular some basic constraints, such as existence of the solution for inverse kinematics of legs, limitation of joint angle range, limitation of joint angle velocity, collision between links and so on, have to be satisfied through out the entire gait cycle. However the trajectories are not uniquely defined by these constraints. To determine the most suitable trajectory in an optimization, we have to select some possible cost functions, e.g. the energy consumption, the global stability and etc. Stability is a basic requirement of gait generation for the biped robot. There are two measurements for stability, static stability and dynamic stability. For static stability, it just requires that the center of gravity (CG) is within robot support area. But this case assumes robot moves very slowly so that the moments from reciprocating links can be neglected and the CG is consistent with center of pressure (CP). For dynamic stability, CP may be different from CG. Because it considers dynamic effects of the robot, the CG may lie outside of the support region. Most biped walking planning has been achieving dynamic stability. A popular method called Zero Moment Point (ZMP) [13, 14] has been used as a criterion of walking stability. The ZMP is defined as the point on the ground where the moment causes the ground reaction forces equal to zero. It can also been taken as the CG. Only if the ZMP resides in the support region, the biped robot can walk avoiding falling. Any biped walking planning has to abide this basic principle. Another basic requirement for trajectory planning is to achieve smooth …