Optimal Energy Consumption Trajectory Planning And Tracking Control For Two-wheeled Self-balancing Robot

With the further development of mobile robot technology and the rise of new fields such as autonomous driving and intelligent express delivery,mobile robots are faced with more and more complex tasks.Under the limited on-board battery,the working time and operating range of the robot are not enough to complete these tasks.How to optimize the energy consumption of the system and complete the assigned tasks as efficiently as possible is an important method to improve customer satisfaction and reduce operating costs.It also conforms to the global environment of energy conservation and emission reduction.Among them,the path planning method enables the robot to complete the moving task with minimum energy consumption to reach the designated destination,which is the core technology to realize the expansion and extension of the moving range and work cycle,and has a good research prospect.However,for mobile robots with different types and functions,the existing energy consumption optimization trajectory planning methods are different.Some methods ignore the non-moving energy consumption caused by sensors and control circuits and do not optimize the running time.Some methods only take distance optimization or trajectory smooth optimization as the standard,without considering the contradictory relationship between friction energy consumption related to running distance and state change energy consumption related to trajectory smoothness.Moreover,most methods consider path planning and trajectory tracking control separately,ignoring that the actual trajectory and the expected trajectory energy consumption caused by the dynamic response of the controller are not exactly the same,making the energy consumption model established inaccurate.In addition,most of the existing methods are based on the established energy consumption model to obtain the optimal trajectory through one-by-one search or iterative optimization of the trajectory,which requires a huge amount of calculation and is difficult to solve.Aiming at the common problems such as inaccurate energy consumption model and difficult optimization solution caused by the above reasons,this paper takes two-wheeled self-balancing robot as the research carrier.Considering the influence of the dynamic characteristics of the controller on energy consumption,the trajectory planning is combined with the motion control model composed of the trajectory tracking controller and the dynamic equation of the robot and an energy consumption model based on frequency domain analysis which can accurately predict robot energy consumption is proposed.And an energy consumption optimal path planning algorithm is proposed for flat and fully known operating environment,so as to improve the energy saving of mobile robot system.In order to reduce the influence of the variation of ground friction coefficient on the accuracy of the algorithm,the on-line dynamic identification strategy was adopted to dynamically update the energy consumption model and the parameters of the controller,so as to improve the robustness of the algorithm to the environment and ensure the optimal energy consumption of the obtained trajectory.The main achievements are summarized as follow:(1)For the trajectory tracking controller,a LQR-PID optimal balance and trajectory tracking algorithm is proposed by combining the classical LQR and PLD algorithm.This algorithm combines the advantages of both methods,which has good dynamic and static characteristics and has less control energy consumption.The simulation results show the control algorithm can keep the robot in balance and track the set system states well and it has strong universality and anti-interference ability.(2)For the energy consumption model,by analyzing the advantages and disadvantages of the classical energy consumption optimal trajectory planning algorithm,it is concluded that it is not enough to consider energy consumption optimization only under the framework of linear trajectory or completely smooth trajectory.Therefore,a new expected trajectory expression is proposed by combining the two.Considering the dynamic characteristics of the controller,the energy consumption of the actual trajectory is not exactly the same as the expected trajectory obtained by the trajectory planning,so an energy consumption model based on frequency-domain analysis is proposed based on parseval's theorem.The model takes full account of the dynamic response of the controller and the energy consumption of non-mechanical components such as sensors,and can accurately reflect the relationship between the desired trajectory and the energy consumption of the robot.(3)For the optimal energy consumption trajectory planning,the global path planning algorithm and the local trajectory planning algorithm are designed respectively.For the global path planning,the distance criteria in A*algorithm is replaced with the criteria related to energy consumption,and the distance factor for obstacle is considered.For the local trajectory planning,based on the relationship between the states of the arc trajectory,the dimension of the energy consumption model is reduced to a function containing only the two variables of the trajectory corresponding to the central Angle and the running time through certain mathematical transformation.Then,the optimal trajectory can be obtained directly by simple mathematical derivation,without searching or iterative optimization for the trajectories that meet the requirements one by one,which greatly accelerates the solving speed.Considering the influence of ground friction coefficient on energy consumption model and controller,an online dynamic identification strategy is proposed.The energy consumption model and controller parameters are dynamically updated by using the dynamic weighted least square method,which improves the robustness of the algorithm to the environment(4)The simulation platform based on MATLAB/Simulink was established and the experimental study of the above method was carried out.Experimental results show that the accuracy of the energy consumption model proposed in this paper is more than 99%,which can accurately reflect the energy consumption of the system.Compared with the commonly used energy consumption optimal cubic Bessel curve method and the shortest distance method,the energy saving rate of the energy consumption optimal trajectory planning algorithm proposed in this paper is increased by 7.8%and 4.5%respectively,and the energy saving effect is significantly improved.In addition,the LEGO EV3 two-wheeled self-balancing robot and wireless positioning system are combined to build a physical platform,which provides conditions for the subsequent physical experiments.