Research On The Trajectory Planning Of Mechatronic Systems Under Kine-Matic And Dynamic Constraints

In the modern industrial applications,mechatronic systems including CNC machines,robots and electro-hydraulic servo systems are required to perform motion tracking tasks in a high-accuracy and high-productivity manner.In the motion tracking tasks,to satisfy the high-productivity requirement,mechatronic systems are required to carry out the motion tracking tasks as fast as possible.However,actuators of practical mechatronic systems are subject to various kinematic and dynamic constraints.Specifically,kinematic constraints mainly refer to that the maximum ve-locity,acceleration and jerk of the actuators are limited,while dynamic constraints mean that the actuators' maximum actuating forces or torques and the corresponding derivatives of the forces or torques are bounded.Increasing the feedrate is benefit to achieving a high-productivity motion tracking performance,which however may also result in violating those kinematic and dynamic constraints above.Once constraints violations occur,the motion tracking controllers of mecha-tronic systems may saturate,which may further lead to significant deteriorations of the motion tracking accuracy and even instability of the whole control system.Consequently,it is a chal-lenging issue for fthe motion tracking of mechatronic systems to achieve the performances of high accuracy and high productivity simultaneously.To achieve the high-accuracy and high-productivity motion tracking performance of mecha-tronic systems,this dissertation deeply investigates the time-optimal trajectory planning issue of mechatronic systems under kinematic and dynamic constraints.Based on various motion track-ing applications of mechatronic systems,this dissertation summarizes the following three types of time-optimal trajectory planning issues:(1)minimum-time off-line trajectory planning along a specified geometric path under kinematic constraints;(2)time-optimal on-line trajectory plan-ning of the desired command trajectory under kinematic constraints;(3)time-optimal on-line trajectory planning of the desired command trajectory in the presence of kinematic constraints,dynamic constraints,parametric uncertainties and uncertain nonlinearities existing in the system's dynamic model.To resolve the three above-mentioned trajectory planning issues,this dissertation proposes the following three types of trajectory planning algorithms respectively:(1)a back and forward check operation based time-optimal off-line trajectory planning algorithm under velocity and accelerations constraints;(2)a novel on-line trajectory planner under velocity and accelera-tion constraints;Moreover,to deal with the online planning issue in which the original command trajectory is generated online and its mathematical expression is unknown,a general on-line tra-jectory planner is further proposed;(3)an integrated algorithm of time-optimal on-line trajec-tory planning in the outer loop and adaptive robust control in the inner loop in the presence of kinematic constraints,dynamic constraints,parametric uncertainties and uncertain nonlinearities existing in the system's dynamic model.The above-mentioned trajectory planning algorithms guarantee the high-accuracy and high-productivity motion tracking performance in the various applications of mechatronic systems eventually.This dissertation consists of the following six chapters:In Chapter 1,the background of the trajectory planning under kinematic and dynamic con-straints is introduced.Additionally,this chapter reviews the state of the art of various off-line and on-line trajectory planning algorithms under kinematic and dynamic constraints,and also summa-rizes the challenging issues of the trajectory planning under kinematic and dynamic constraints.Finally,an outline of the dissertation's contributions and contents is presented.In Chapter 2,as for the demand on multi-axis mechatronic systems tracking a specified con-touring path in a high-accuracy and high-productivity manner,a back and forward check operation based time-optimal trajectory planning algorithm with high off-line computational efficiency is proposed under kinematic and dynamic constraints of practical mechatronic systems.Based on the path-velocity decomposition(PVD)framework,this algorithm first transforms the velocity and acceleration constraints of mechatronic systems to the corresponding constraints on the para-metric velocity and parametric acceleration,and then optimizes the trajectory in the parameter space.Afterwards,the optimal analytic solution of the parametric velocity at each node can be obtained directly by four lemmas which are developed by the proposed trajectory planning al-gorithm.Meanwhile,simulations of the trajectory planning algorithms on a Lissajous curve are carried out,and the simulation results confirm the time optimality of the proposed back and for-ward check operation based trajectory planning algorithm.Finally,to demonstrate the benefits of the proposed trajectory planning algorithm to the practical contouring tracking tasks of multi-axis mechatronic systems,several comparative contouring tracking experiments are conducted on a biaxial linear motor driven system.The experimental results indicate that the proposed trajectory planning algorithm can indeed achieve the high-accuracy and high-productivity performances si-multaneously in the contouring tracking tasks.In Chapter 3,as for the issue of online planning the desired command trajectory in the mo-tion tracking applications of multi-axis mechatronic systems,a novel on-line trajectory planner is devised to modify the desired command trajectory online so that the planned trajectory satisfies the velocity and acceleration constraints of mechatronic systems.The proposed novel on-line trajectory planner consists of a bound estimator and novel nonlinear filter.Specifically,the bound estimator transforms the velocity and acceleration constraints of mechatronic systems into the corresponding constraints on the parametric velocity and parametric acceleration,respectively.Afterwards,the desired time-varying parameter trajectory is online planned by the novel nonlin-ear filter under the transformed parametric velocity and parametric acceleration constraints.In particular,the devised on-line trajectory planner removes the limitation of previous on-line trajec-tory planners that the upper and lower bounds of the parametric acceleration must be positive and negative respectively.As such,more general parametric acceleration constraints can be handled by the proposed novel on-line trajectory planner.Additionally,to deal with the potential stability issues existing in the on-line trajectory planner,an on-line critical test curve algorithm is further proposed in this chapter.To verify the effectiveness of the proposed on-line trajectory planner and critical test curve algorithm,several comparative contouring tracking experiments are carried out on a biaxial direct-driven system.The experimental results indicate that the planned trajectory respects system's velocity and acceleration constraints strictly all the time and the high-accuracy contour tracking performance is guaranteed eventually.In Chapter 4,to address the issue of online planning the original command trajectory with unknown mathematical expression,on the basis of the novel on-line trajectory planner and criti-cal test curve algorithm developed in chapter 3,this chapter proposes a general on-line trajectory planner and improved critical test curve algorithm.In the design of the general on-line trajec-tory planner,an on-line interpolator is first devised to formulate the online generating original command trajectory with unknown mathematical expression in the PVD form.Afterwards,the interpolated trajectory is online planned by the novel on-line trajectory planner developed in chap-ter 3.Furthermore,note that the global knowledge of the original command trajectory considering in this chapter is not available in advance.To guarantee the stability of the devised general on-line trajectory planner,this chapter proposes an improved critical test curve algorithm.To validate the effectiveness of the proposed general on-line tra.jectory planner and improved critical test curve algorithm,several comparative experiments are conducted on a master-slave tele-robotic system.The experimental results indicate that the proposed on-line trajectory planner and improved crit-ical test curve algorithm are capable of online planning the original cormmand trajectory with unknown mathematical expression and also resolve the stability issues existing in the on-line tra-jectory planner.In addition,the planned trajectory fulfills the system's velocity and acceleration constraints strictly,and the motion tracking performance of the slave robot is guaranteed eventu-ally.In Chapter 5,besides the kinematic constraints considered in the previous chapters,the dy-namic constraints of mechatronic systems are further taken into consideration.Moreover,the dynamical models of practical mechatronic systems suffer from parametric uncertainties and un-certain nonlinearities.Taking a linear motor driven system as the case study,this chapter develops an integrated algorithm of time-optimal on-line trajectory planning in the outer loop and adaptive robust control in the inner loop.Specifically,the adaptive robust control algorithm devised in the inner loop is employed to deal with the parametric uncertainties and uncertain nonlinearities ex-isting in the dynamics of the linear motor.Meanwhile,the dynamic constraints on the referenced trajectory is established in the development of the adaptive robust controller.In the outer loop,an on-line trajectory planning algorithm is designed to online plan the original command trajec-tory under kinematic constraints and the dynamic constraints established in the inner loop so that the planned trajectory converges to the original command trajectory in minimum time.To ver-ify the effectiveness and superiority of the proposed algorithms,several comparative experiments are carried out on a single-axis linear motor driven system.The experimental results indicate that the proposed integrated algorithm can achieve minimum-time transient response and high-accuracy steady-state motion tracking performances simultaneously in the presence of kinematic constrains,dynamic constrains,parametric uncertainties and uncertain nonlinearities existing in the linear motor driven system.In Chapter 6,the research work of this dissertation is summarized.Furthermore,conclusions and innovations are highlighted,and some future researches are discussed.