Trajectory Tracking Control Of Spherical Robot With Input Saturation And Time Delay

Compared with other traditional mobile robots,spherical robots have unique advantages such as flexible movement,low energy consumption and low impact from harsh environment.Therefore,they have a broad application prospect in anti-terrorism,complex terrain detection and outer space exploration.However,the control problem of spherical robots has become one of the main factors hindering its wide application.The trajectory tracking problem is the most common problem for spherical robots in practice,and also an important control problem of spherical robots.In this paper,a pendulum-driven spherical robot with stereo vision is chosen as the research object.The work of this paper mainly focuses on the trajectory tracking controller design of the spherical robot with input saturation and state feedback delay due to visual camera installation.Besides,the stability and effectiveness of the controller are theoretically analyzed and simulated.The main research contents of this paper are as follows:Firstly,the dynamic model of the spherical robot is established theoretically based on Routh equation because of its convenience to construct the equation of state.Then,the accuracy of the model is illustrated by the comparison between MATLAB simulation and ADAMS virtual prototype simulation.In order to facilitate the controller design process,the corresponding control model is obtained by simplifying the model based on reasonable assumptions.Secondly,PID algorithm is widely applied in practice due to its simple structure.However,it is seldom used in trajectory tracking control of spherical robots.PID algorithm cannot meet the needs of trajectory tracking of spherical robots only by itself.Therefore,PID control method is combined with adaptive control in this paper.The controller is divided into inner and outer loop by designing a virtual PI controller in the outer loop.A PI controller is designed in the inner loop to realize the trajectory tracking control and an adaptive law is introduced to estimate disturbances.Then,the stability of the system is shown.Compared with the existing PID controller with the same structure,it shows that the proposed algorithm has higher tracking accuracy.Thirdly,the input saturation is not involved in the research on trajectory tracking control of spherical robot at present,but the influence of input saturation on spherical robot system cannot be ignored.Therefore,the input saturation is added to the trajectory tracking problem of spherical robot in this paper.A trajectory tracking controller is designed based on Lyapunov function.The input saturation is compensated by an auxiliary system,and the external disturbance is handled by a disturbance observer.Then,the stability of the system is analyzed.Simulation results show that the proposed controller has smaller tracking error and smoother input torque signal.To study the trajectory tracking control problem of the spherical robot with feedback delay,the condition of partial feedback state with delay is considered first.In order to ensure the robustness of the system while observing the feedback states with time delay,a sliding mode observer is designed in this paper.Meanwhile,the input saturation is taken into account and an auxiliary system is designed to compensate for it.Based on the Lyapunov function and the state observed by the sliding mode observer,a trajectory tracking controller is designed.The effectiveness of the trajectory tracking controller is verified by simulation results under different time delays and an approximate range of time delay is given when the input torque signal is relatively smooth,which provides a reference for the engineering application of the algorithm.Finally,the feedback time delay problem is further extended to the case where time delay exists in all feedback states and the problem is transformed into the input delay problem.In order to ensure the robustness of the system to external disturbances and time delay,a trajectory tracking robust controller is designed based on the Lyapunov function and the mean value theorem,and an auxiliary system is designed to compensate both input saturation and time delay.An approximate range of the time delay is determined by the simulation with different time delays,which satisfies the trajectory tracking effect and ensures the relative smoothness of the input signal,and thus provides a reference for the engineering application of the algorithm.There are 47 figures,6 tables and 91 references in total.