Research On Motion Planning For Cable Robots

Cable robots use flexible cables to manipulate the end-effector,since cables can only pull but cannot push the end-effector,the motion planning of cable robots is considered to be a significant challenge.To overcome the blindness of motion planning,first,a geometric approach is first used to plan feasible trajectories for simple point-mass cable robots,then the approach is extended to plan trajectories for platform cable robots.After that,a more general motion planning approach which is less sensitive to the mechanism characteristics is studied from a mapping perspective.Finally,mechanisms are designed based on the desired motion space and trajectory realization is considered under various uncertainties.The contents of this dissertation are detailed as follows.1)Motion planning for point-mass cable robots:To determine the existence of feasible trajectories,a geometric approach is proposed to analyze the properties of dynamics constraints and the corresponding dynamic workspace.First,by using analytic geometry and projective geometry,the complex tension constraints are transformed into simple feasible regions on the position-acceleration plane.Then,the maximum feasible range of motion of the end effector is determined according to the boundaries of the feasible regions on the plane,which can be used to define dual workspaces(reachable workspace and returnable workspace).After that,feasible paths are designed analytically by using the dual spaces,and feasible point-to-point trajectories,periodic trajectories,and transition trajectories are designed directly on the position acceleration plane.The corresponding non-empty feasible ranges of trajectory parameters can be determined analytically according to the boundaries of the feasible regions.2)Motion planning for platform cable robots:To apply the geometric approach to platform mechanism,the rotation along principal axes of inertia is first analyzed considering the unilateral tension transmission properties of cables,which can also be transformed into feasible regions on the position-acceleration plane,however,the boundaries of the feasible regions become much more complex.According to the realizability condition of curves designed on the plane,reachable workspaces are analyzed and point-to-point trajectories are designed on the plane.For the case of rotation along general axes,inclusive trajectories which are comparable in size can be used to explore the boundaries of reachable workspaces,and the range of point-to-point trajectory parameters can be obtained numerically by discretizing the path.Periodic trajectories can be planned similarly through composition of basic functions or basic motions,and the ranges of parameters of basic functions/motions can be used to describe the corresponding trajectory space.Finally,some conclusions or hypotheses about the existence of transition trajectories are given,and transition trajectories between the two states are designed by applying probabilistic exploring tree(PET)algorithm which selects tree nodes to match desired states according to dynamic priority.3)General motion planning less sensitive to cable robots' types:To search feasible trajectories meeting practical needs and improve the performance of feasible trajectories,dual mappings(feasibility preserve mapping and feasibility variance mapping)are defined and applied to planning general dynamically feasible trajectories.The feasibility variance mapping method first maps tension constraints into the rootless region of the tension boundary equation,then makes the real solution of the tension boundary equation leave the infeasible region by applying a PET based root relocation algorithm,such that infeasible trajectories originally designed are modified into feasible trajectories.The feasibility preserve mapping method uses Sturm's theorem,interval arithmetic,or continuous extremum tracing technique to transform the tension constraints of parameterized feasible trajectories into constraints on trajectory parameters,which can be used to dynamically improving the trajectory performance under certain criterion or obtaining the range of trajectory parameters used to describe the trajectory space.4)Mechanism design and trajectory realization of cable robots:To achieve the desired motion in simulations or experiments,the reachable workspace and static workspace of cable robots are described by dual curves defined through extension mapping and mechanisms are then designed properly through contraction mapping of the desired reachable space.To stop the end-effector safely when it is unable to track moving targets,the cable tension constraints are mapped into constraints on a generalized center varying field described by a linear time varying differential equation whose coefficients are discontinuous functions of time.Then,by applying the PET algorithm with different extending priorities for vertical tree branches and horizontal tree branches,the coefficients of the differential equation are properly selected considering tension constraints,constraints on the generalized center of the field,and the asymptotic stability condition.As a result,a series of locally feasible trajectories are generated,which makes it possible for the end-effector to stop without suffer cable slackness.This dissertation focuses on using geometric approach to define and obtain the reachable workspaces in which the existence of feasible motions can be guaranteed,and plan feasible trajectories considering complex dynamics constraints in the reachable workspaces.The validities of representative methods proposed are finally verified through simulations/experiments.