Research On Dynamic Trajectory Planning For Fully-actuated Cable-suspended Parallel Robots

Cable suspended parallel robots(CSPRS)are a kind of parallel robot which uses multiple parallel cables to drive the suspension moving platform.It is an important type of cable driven parallel robot.Thanks to the light weight of the cable and high extensibility ratio,the cable suspended parallel robot has the outstanding advantages of large working space,low inertia,high dynamic performance,and high load-mass ratio,and are widely used in the fields of motion simulator,giant astronomical telescope,large-scale material addition manufacturing and logistics handling.The unilateral tension constraint of the cable is the most fundamental problem in the research of the cable suspended parallel robot.Due to the existence of the dynamic constraint of the tension,the trajectory planning of the cable suspended parallel robot needs special research.In this paper,the dynamic trajectory planning of cable suspended parallel robots is studied.The CSPRs is used as the dynamic control system to planning the dynamic trajectory beyond the static workspace of the CSPRs,so that the motion range of the CSPRs exceed the horizontal projection of the robot base,thus expanding the working space of the CSPR s.At present,most researches limit the motion of the CSPRs to its static workspace.Under this assumption,the reachable range of the end effector of CSPR s is usually less than the horizontal projection range of its base.In the static workspace,the gravity of the moving platform can maintain the tension of the cable,while the dynamic trajectory uses the inertial force and gravity of the moving platform to maintain the tension of all the cables,which breaks through the limit of the static workspace.In this paper,based on the kinematic and dynamic models of CSPRs and t he tension constraint,the acceleration constraint of the moving platform when the motion exceeds the static workspace of the robot is analyzed.The feasible acceleration direction of the moving platform becomes narrower and narrower as it moves beyond the static workspace,and it is only feasible in the direction pointing to the static workspace.Based on the optimal control theory,through the position velocity phase diagram of two degrees of freedom CSPR optimal time along with the horizontal straight line swing motion,it is found that for the CSPRS with limited control input,the total energy stored in the dynamic system can be gradually increased by accumulating multiple swing motions conforming to the tension constraint,so that the swing of the moving platform is far beyond the static working space.Aiming at the problem that the existing point-to-point trajectory planning methods can only produce a finite number of oscillations,this paper proposes a point-to-point dynamic trajectory planning method based on the basic trajectory and random tree search algorithm,which is driven by three cables and three degrees of freedom point mass CSPRs.In order to solve the problem that the existing planning methods can only produce special kinds of periodic motion and transition motion trajectory,a method of nonharmonic periodic dynamic trajectory planning and transition dynamic trajectory planning based on linear time-varying model predictive control for three translational motion CSPRs is proposed.Firstly,the dynamic model of three translational motion CSPRs is linearized globally based on the feedback of cable length,and the time-varying linear dynamic model is obtained.According to the linear system equation.An optimization algorithm based on linear progr amming is proposed,which can generate general anharmonic periodic motion under tension constraints.By decoupling the Cartesian space acceleration constraint of the moving platform,a two-step transition trajectory design method is proposed.Firstly,the parametric equation of the periodic transition trajectory in the direction of gravity in the Cartesian coordinate system is given,and a general periodic transition trajectory planning algorithm for three translational motions is established.For the dynamic trajectory planning of point-to-point motion,period and transfer motion of 6-DOF CSPRs,the dynamic characteristics of 6-DOF CSPRs are analyzed by using feasible force screw cone,and the similarity relationship between low-dimensional and high-dimensional CSPRS is established,and the optimal initial values of three translational trajectories of 6-DOF CSPRs are generated by using 3-DOF CSPRs.The normal form of point-to-point,period,and transfer trajectory optimization problem of 6-DOF CSPRs is established,and the solution process of transforming it into the standard form of NLP problem is based on Chebyshev polynomials is given.A general dynamic trajectory optimization algorithm for 6-DOF CSPRs is proposed.Finally,the CSPR experimental system and the cable length tracking controller based on tension feedback are designed.Using the experimental system and the external motion capture system,the dynamic trajectory of the previous planning is verified on the three degrees of freedom point mass CSPR experimental system and the six degrees of freedom CSPR experimental system,which proves the feasibility and accuracy of the trajectory obtained by the planning algorithm in the actual robot system.In this paper,the research on dynamic trajectory planning of CSPRs provides a solid theoretical basis for the expansion of CSPRs workspace and expands the application scenarios of CSPRs in motion simulator and other fields.The research results of this paper have certain theoretical guiding significance and en gineering practice value for CSPRs trajectory planning research.