Research On Trajectory Planning Of Mobile Robot Based On Geodesic

With the rapid development of mobile robot technology,trajectory planning has become a hot issue.Traditional trajectory planning can meet the trajectory requirements of mobile robots in most cases,but the evaluation indicators such as trajectory length,motion time and energy consumption often cannot reach the optimal values.As the local shortest line in the two-dimensional space and multi-dimensional space,the geodesic line conforms to the index of the optimal trajectory length.To this end,this paper proposes a geodesic-based trajectory planning method for mobile robots.Under the given initial conditions,the optimal trajectory planning with the shortest path or the least energy consumption is carried out.Its contents are as follows:(1)Taking the rotation angle of the driving wheel of the differential driving mobile robot as parameters,the Riemannian metric of the square of the arc length of the robot trajectory is constructed,and using this Riemannian metric to solve the Christoffel symbolic component that conforms to the parameters of the wheel rotation angle of the robot,and then the geodesic equation including the rotation angle variable is obtained.Finally,the geodesic equation is solved under the given initial value condition,and the optimal geodesic trajectory with the shortest path is obtained.(2)Based on Python programming,the Christoffel symbolic component containing the wheel angle variable of the robot and the geodesic equation representing the shortest path are solved,and then the geodesic algorithm is constructed.By setting three different initial conditions,the relationship diagram of the rotation angle and arc length parameters,the change relationship diagram of angular velocity and arc length parameters,the geodesic trajectory diagram in two-dimensional space and the change relationship diagram of joint space are obtained.Comparing the planning results of three different initial conditions,the robot trajectory solved by the algorithm in this paper conforms to the geodesic property in the two-dimensional Euclidean space,which ensures that the motion of the robot along the geodesic line in the two-dimensional Euclidean space without obstacles is stable(3)Three combinations of starting points and ending points are set to compare the trajectory planning performance of the RRT algorithm and the geodesic algorithm in a two-dimensional map with known obstacles.The simulation results show that under the condition of the same maximum number of iterations,the trajectory length of the geodesic algorithm is shorter than that of the RRT algorithm,which is in line with the characteristics of the optimal trajectory length.(4)Research on the trajectory planning implementation of geodesic algorithm in ROS(Robot Operating System).Build a four-wheel differential drive robot model and an indoor environment model,control the robot to receive environmental information to generate a two-dimensional map;improve the geodesic algorithm to enable mobile robot to bypass circular obstacles;build an improved geodesic algorithm global planner,compared with the global planner of the A* algorithm.The simulation results show that the improved geodesic algorithm has the characteristics of short path length,less turning times,short movement time and low energy consumption.