Trajectory Planning And Robust Control Of A 3-DOF Underactuated Manipulator

Systems where there are more dimensions of generalized coordinates than the number of control inputs are defined as underactuated systems.Underactuated manipulators are widely used in industry,medicine,military and other fields due to their high efficiency,flexibility and light-weight.Besides,underactuated manipulators can work in extreme environments.The research on trajectory planning and robust control of underactuated manipulators is one of the hotspots in the field of robotics,artificial intelligence,control theory and technology.It can not only provide safe and effective control schemes for the tail end of manipulators but also promote the development and improvement of control theory and technology of the nonlinear nonholonomic systems.Due to the coupling between the states or the accompanying nonholonomic constraints,it is a challenging task to plan the trajectory and design the control algorithm for the underactuated system.The controlled plant of this thesis is a three degree-of-freedom helicopter system.If the center of the two driven motors is regarded as the controlled position of the tail end of the manipulator,the system is a typical underactuated second-order nonholonomic system,which is suitable for advanced control theory and technology teaching and experimental verification.In this thesis,firstly,the multi-rigid-body dynamic model of the three-dof helicopter is established.Then normalization processing of the model is carried out to reduce the number of parameters,and the parameters of travel,elevation and pitch channels are fitted respectively.The simulations and experiment environments are built to compare the response of the system.The results show that the identified model can describe the dynamics of the 3-DOF helicopter platform approximately and is more accurate than the original model.However,the response of the identified model still has some deviation in the transient and steady-state accuracy compared to the actual platform.For the second-order nonholonomic system,the virtual constraints between the original generalized coordinates are constructed by using the virtual holonomic constraint(VHC)method,and then the identified model is reduced to the virtual constrained system.There exists a feedback control law that makes the constraints invariant along the solutions of the closed-loop system.According to the desired helicopter motion,three kinds of virtual constraints are defined,and three typical trajectories of the helicopter are calculated offline to serve as the reference signals of tracking control.Based on the identified model and the reference trajectories from the route planning module,a robust high-precision tracking controller for the tail end track is designed.Firstly,feedback linearization is applied to obtain a linear system.Then the inner-outer loop control structure is used and the controller parameters are determined by the desired error trajectory model.Finally,a novel robust controller is proposed in combination with the uncertain and disturbance estimator(UDE)to compensate for the influence of inaccurate modeling and identification factors on the control accuracy of the system.The stability of the closed-loop system is demonstrated and the key factors affecting tracking errors are analyzed.To validate the trajectory planning scheme and the robust trajectory tracking control scheme,simulations and experiments are carried out.At first,the simulation model is built in Matlab/Simulink to verify the effectiveness and the property of interference and noise suppression of the robust control law.The necessity of trajectory planning for nonholonomic systems and the advantages of combining offline planning with online planning are illustrated through simulations in different reference signals.At last,the design scheme is run on the Googoltech three degree-of-freedom helicopter platform,and the closed-loop experiments of the system and result comparison are carried out.The experimental results show that the tracking errors of the controlled system are bounded for the three planning trajectories and the steady-state errors are reduced by using uncertain and disturbance estimators,therefore the effectiveness of the robust control law is verified.Further,the reliability and applicability of the identified model are validated for the planning trajectories based on the model are safe and feasible.