author ： 19 the lz

date ：2021-11-3

The paper ：《Robust and Efficient Quadrotor Trajectory Generation for Fast Autonomous Flight》

problem :

Under the condition of limited time and airborne computing resources , The existing work can not guarantee the generation of safe and feasible dynamic trajectory with high success rate .

contribution :

(1) A set dynamics path search algorithm is proposed 、b A robust and efficient method integrating spline optimization and time adjustment .
(2) A new method based on b Optimization formula of spline convex hull characteristics .
(3) A method based on derivative control points and non-uniform control points is adopted b Adjustment method of spline time allocation .

One 、 background ：

Two 、 Related work ：

Hard constraint method

The global optimality is guaranteed by convex form . However , Ignoring the distance from obstacles in free space , This often causes the trajectory to approach obstacles . Besides , Dynamic constraints are conservative , Make the track speed insufficient , Fly fast .

Soft constraint

Methods using gradient information to push the trajectory away from obstacles , But there is a local minimum problem , There is no strong guarantee of feasibility and success rate . Our optimization method also uses gradient information to improve the security of trajectory . However , It is different from the previous methods of calculating expensive integration along the trajectory line , be based on b Convex hull properties of splines , Make the formula simpler . It greatly improves the computational efficiency and convergence speed .

3、 ... and 、 Research process and results ：

Front end trajectory generation

Purple line : Because the end of the search is difficult to just fall on the target , Each time from open set After the node pops up , Calculate a track from the current point to the end point , If the trajectory passes the safety and feasibility check , The search is terminated in advance .

Sports primitives

Using the optimal control formula to generate motion primitives

heuristic

Using Pontryagin's minimum principle , To calculate the J(t) To minimize the xc To the target state xg Track of

Back end trajectory optimization

B Spline trajectory optimization

The trajectory consists of b Spline representation (pb = 3).
Its first derivative ( Speed ) Still convex .

The red curve is the initial path , The green curve is optimized b Splines . Yellow nodes representative b Control points of splines . Because the distance information is ignored , The initial path approaches the obstacle , Need to combine gradient information , use B Spline optimization pushes the trajectory away .

Loss function

Smoothness guarantee

Make the track smooth

Reliability guarantee

d(Qi): The distance from the control point to the nearest obstacle
Move the track away from the obstacle

Dynamic feasibility guarantee

Time adjustment

The basic reason is that gradient information tends to lengthen the whole trajectory , And push it away from obstacles . therefore , The original time allocation may make some trajectories infeasible ( Excessive speed and acceleration ).

resolvent : Make time adjustments , To make the velocity and acceleration on the trajectory below the maximum limit

It is assumed that the control point of the speed curve exceeds the feasibility constraint , You only need to control the interval of the node vector between the initial control points , You can reduce the part that exceeds the speed threshold .

If , Then speed will be feasible . because :

Acceleration optimization is the same .

Overall process

Is to calculate the motion primitive at each point , Then iterate the points in the motion primitive to calculate the motion primitive , In this process, use A Algorithm to calculate and search the path . And then use it b Spline curve to match the obtained A Path optimization .

result

The front-end trajectory generates contrast :

Back end trajectory optimization comparison :

conclusion

A novel on-line motion planning method for four rotor autonomous navigation is proposed in this paper . The online fast motion planning problem is decomposed into front-end dynamic path search and back-end nonlinear trajectory optimization . The dynamic path search algorithm is used to find the safe path 、 Dynamic feasible and shortest initial path , The smoothness and gap of the initial path are further improved by gradient optimization algorithm .