A Survey On Trajectory Planning For Parallel Collaborative Mechanism

In collaborative trajectory planning for parallel collaboraing mechanismsresearch areas there are few relative research reports yet at home and aborad. As anexploratory subject, this paper has made a in-depth study on the inverse kinematics，working space and the whole process of collaborative trajectory planning forparallel collaborating mechanism based on the simulation platform consist of twoparameter-given stewart mechanism.This thesis uses NURBS to represent the collaborative surface considering thearbitrariness of collaboration surface and then analysis NURBS surface modelingand real-time interpolation. The most difficulty of NURBS surface shaping istrimming while the core of NURBS surface timming is the projection of thethree-dimensional coordinate space to the uv parameter space. A fast trimmingmethod based on Newton iteration is proposed in this paper and it solved thetrimming problem effectively. For interpolation, a method to analysis real-timeinterpolating for collaborative mechanism combined self-adjusting parameters toget step u and adaptive speed to get step v is proposed in this paper.A collaborative optimization model is designed in this paper, which is the coreof the subject and can be described as a model which is based on three time-varyingoptimization parameters to decompose and allocate the collaborative task,translating the problem of collaborative task decompositon and allocation into anoptimized problem. Aiming at the position of the parallel collaborative mechanism(including the positional information and the posture angle information), thepositional collaborating of the collaborative mechanism that is to decompose andallocate the translation matrix of the collaborative mechanism in a optimized way iscompleted.A collaboration trajectory planning simulation software using GTK+andOpenGL under linux system is developed with the aim to display the process ofcollaboration trajectory planning and to validate the feasibility and correctness ofthe algorithms based on the algorithms of the NURBS collaborative surfacemodeling, real-time interpolation and collaborative optimization model.