최적 경로 계획을 위한 RRT^*-Smart 알고리즘의 개선과 2, 3차원 환경에서의 적용

Improvement of RRT^*-Smart Algorithm for Optimal Path Planning and Application of the Algorithm in 2 & 3-Dimension Environment

Abstract

Optimal path planning refers to find the safe route to the destination at a low cost, is a major problem with regard to autonomous navigation. Sampling Based Planning(SBP) approaches, such as Rapidly-exploring Random Tree Star($RRT^*$), are the most influential algorithm in path planning due to their relatively small calculations and scalability to high-dimensional problems. $RRT^*$-Smart introduced path optimization and biased sampling techniques into $RRT^*$ to increase convergent rate. This paper presents an improvement plan that has changed the biased sampling method to increase the initial convergent rate of the $RRT^*$-Smart, which is specified as m$RRT^*$-Smart. With comparison among $RRT^*$, $RRT^*$-Smart and m$RRT^*$-Smart in 2 & 3-D environments, m$RRT^*$-Smart showed similar or increased initial convergent rate than $RRT^*$ and $RRT^*$-Smart.

Fig 1. RRT, RRT* Algorithm

Fig 2. RRT* pseudo code

Fig 3. Path Optimization

Fig 4. mRRT*-Smart pseudo code

Fig 5. Modified beacon node

Fig 6. A comparison of 2-D simulation results. RRT* is shown in (a)-(d), RRT*-Smart is shown in (e)-(f) and mRRT*-Smart is shown in (i)-(l)

Fig 7. Costs against iterations(S=RRT*-Smart, M=mRRT*-Smart)

Fig 8. A comparison of 3-D simulation results at n=2000

Fig 9. Costs against iterations(S=RRT*-Smart, M=mRRT*-Smart)

Fig 10. Nodes at 2000 iterations

Table 1. Simulation setting

Table 2. Bias sampling setting

Table 3. Path planning results at 1000, 1500, 2000 and 2500 iterations for 2-D case 1, 2, 3 & 3000, 3500, 4000, and 4500 iterations for 2-D case 4

Table 4. Path planning results at 1000, 1500, 2000 and 2500 iterations for 3-D Case