Three-dimensional smooth trajectory planning using realistic simulation

This paper presents a method for planning three-dimensional walking patterns for biped robots in order to obtain stable smooth dynamic motion and also maximum velocity during walking. To determine the rotational trajectory for each actuator, there are some particular key points gained from natural human walking whose value is defined at the beginning, end and some intermediate or specific points of a motion cycle. The constraint equation of the motion between the key points will be then formulated in such a way to be compatible with geometrical constraints. This is first done in sagittal and then developed to lateral plane of motion. In order to reduce frequent switching due to discrete equations which is inevitable using coulomb dry friction law and also to have better similarity with the natural contact, a new contact model for dynamic simulation of foot ground interaction has been developed which makes the cyclic discrete equations continuous and can be better solved with ODE solvers. Finally, the advantages of the trajectory described are illustrated by simulation results.