Dynamic Trajectory Planning And Control Of A Cable-driven Parallel Robot

Compared with a link-driven parallel robot,a cable-driven parallel robot(CDPR)possesses advantages of lighter weight,simple structure,low cost,and large workspace,but it has disadvantages such as poor stiffness.This paper proposes a rigid-flexible hybrid cable-driven parallel robot,which is composed of four cables and a rigid link.The rigid link restricts its translational degree of freedoms(DOFs),so the robot only has three rotational DOFs.Due to its light weight,the robot can be used as a grabbing mechanism or a camera steering system for a quadrotor unmanned aerial vehicles(UAVs).In this paper,quaternions are used for rotation representation,and correspondingly the kinematics,statics and dynamics of the cable-driven parallel robot based on quaternions are analyzed.Workspace analysis is the prerequisite for trajectory planning.Therefore,according to the static equations,the static feasible workspace is analyzed applying the convex hull theory and the vector projection theorem.It is concluded that the static feasible workspace gradually becomes smaller when the pre-tightening force of the cables increases.It is found from the dynamic equations that the robot has actuation singular orientations.The actuation singular orientations often appear in the workspace of a cable-driven parallel robot,and thus the workspace is divided into several parts.When the moving platform passes through the singular orientations,there are unresolved and sudden changes in the cable forces,which results in instantaneous loss of stiffness or even loss of control of the robot.Therefore,the existence of the singular orientations of the cable-driven parallel robot reduces its workspace and greatly limits the movement performance of the moving platform.For this reason,consistency conditions that can enable the robot to stably pass through the singular orientations are studied.Besides,the vector inner product form of the consistency conditions is derived,which simplifies the calculation of the consistency condition of a complex parallel robot.In addition,this article also discusses two methods for solving the inverse dynamics,namely the minimum tension optimization method and the least square method.The advantages and disadvantages of each are compared,and finally the tension distribution using the least square method is selected for the dynamics compensation in control.A sequence of target orientations are reached by planning dynamic trajectories using the unit quaternion.A modified spherical linear interpolation with a fifth degree polynomial as the time function is used for the generation of a trajectory which does not contain a singular orientation.Moreover,a transition segment using a seventh degree polynomial is designed to merge into the fifth degree polynomial in order to satisfy the consistency conditions and pass through singular orientations.Simulations are provided to verify the proposed technique.A prototype is built and trajectory tracking is performed using a dynamic feedforward and fuzzy PD controller.The Simulink program is provided,and the voltage analog signal is sent to the servo motor through the Dspace toolbox.The servo motor is in torque control mode,and the feedback signal is the motor encoder value,which successfully realizes the trajectory tracking in the joint space.Dynamic feedforward is added to the controller to keep the positive cable tensions.Since the cable-driven parallel robot is designed as a grasping mechanism of UAVs,it is susceptible to interference from external environmental factors(wind,etc.),so fuzzy control algorithms are added.Fuzzy control is a robust control that can resist external interference well.This paper does a more detailed research on a cable-driven parallel robot from kinematics analysis,dynamic analysis,to dynamic trajectory planning and control.It provides an important theoretical and experimental basis for the practical application of the mechanism.