18 research outputs found
The Critical Radius in Sampling-based Motion Planning
We develop a new analysis of sampling-based motion planning in Euclidean
space with uniform random sampling, which significantly improves upon the
celebrated result of Karaman and Frazzoli (2011) and subsequent work.
Particularly, we prove the existence of a critical connection radius
proportional to for samples and dimensions:
Below this value the planner is guaranteed to fail (similarly shown by the
aforementioned work, ibid.). More importantly, for larger radius values the
planner is asymptotically (near-)optimal. Furthermore, our analysis yields an
explicit lower bound of on the probability of success. A
practical implication of our work is that asymptotic (near-)optimality is
achieved when each sample is connected to only neighbors. This is
in stark contrast to previous work which requires
connections, that are induced by a radius of order . Our analysis is not restricted to PRM and applies to a
variety of PRM-based planners, including RRG, FMT* and BTT. Continuum
percolation plays an important role in our proofs. Lastly, we develop similar
theory for all the aforementioned planners when constructed with deterministic
samples, which are then sparsified in a randomized fashion. We believe that
this new model, and its analysis, is interesting in its own right
On the performance of random linear projections for sampling-based motion planning
Sampling-based motion planners are often used to solve very high-dimensional planning problems. Many recent algorithms use projections of the state space to estimate properties such as coverage, as it is impractical to compute and store this information in the original space. Such estimates help motion planners determine the regions of space that merit further exploration. In general, the employed projections are user-defined, and to the authorsβ knowledge, automatically computing them has not yet been investigated. In this work, the feasibility of offline-computed random linear projections is evaluated within the context of a state-of-the art sampling-based motion planning algorithm. For systems with moderate dimension, random linear projections seem to outperform human intuition. For more complex systems it is likely that non-linear projections would be better suited
ΠΠ΅ΡΠΎΠ΄Ρ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΡΠΈ Π² ΡΡΠ΅Π΄Π΅ Ρ ΠΏΡΠ΅ΠΏΡΡΡΡΠ²ΠΈΡΠΌΠΈ (ΠΎΠ±Π·ΠΎΡ)
Planning the path is the most important task in the mobile robot navigation. This task involves basically three aspects. First, the planned path must run from a given starting point to a given endpoint. Secondly, it should ensure robotβs collision-free movement. Thirdly, among all the possible paths that meet the first two requirements it must be, in a certain sense, optimal.Methods of path planning can be classified according to different characteristics. In the context of using intelligent technologies, they can be divided into traditional methods and heuristic ones. By the nature of the environment, it is possible to divide planning methods into planning methods in a static environment and in a dynamic one (it should be noted, however, that a static environment is rare). Methods can also be divided according to the completeness of information about the environment, namely methods with complete information (in this case the issue is a global path planning) and methods with incomplete information (usually, this refers to the situational awareness in the immediate vicinity of the robot, in this case it is a local path planning). Note that incomplete information about the environment can be a consequence of the changing environment, i.e. in a dynamic environment, there is, usually, a local path planning.Literature offers a great deal of methods for path planning where various heuristic techniques are used, which, as a rule, result from the denotative meaning of the problem being solved. This review discusses the main approaches to the problem solution. Here we can distinguish five classes of basic methods: graph-based methods, methods based on cell decomposition, use of potential fields, optimization methods, ΡΡΠ² methods based on intelligent technologies.Many methods of path planning, as a result, give a chain of reference points (waypoints) connecting the beginning and end of the path. This should be seen as an intermediate result. The problem to route the reference points along the constructed chain arises. It is called the task of smoothing the path, and the review addresses this problem as well.ΠΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΡΡΠΈΒ β Π²Π°ΠΆΠ½Π΅ΠΉΡΠ°Ρ Π·Π°Π΄Π°ΡΠ° Π² ΠΎΠ±Π»Π°ΡΡΠΈ Π½Π°Π²ΠΈΠ³Π°ΡΠΈΠΈ ΠΌΠΎΠ±ΠΈΠ»ΡΠ½ΡΡ
ΡΠΎΠ±ΠΎΡΠΎΠ². ΠΡΠ° Π·Π°Π΄Π°ΡΠ° Π²ΠΊΠ»ΡΡΠ°Π΅Ρ Π² ΠΎΡΠ½ΠΎΠ²Π½ΠΎΠΌ ΡΡΠΈ Π°ΡΠΏΠ΅ΠΊΡΠ°. ΠΠΎ-ΠΏΠ΅ΡΠ²ΡΡ
, ΡΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½Π½ΡΠΉ ΠΏΡΡΡ Π΄ΠΎΠ»ΠΆΠ΅Π½ ΠΏΡΠΎΠ»Π΅Π³Π°ΡΡ ΠΎΡ Π·Π°Π΄Π°Π½Π½ΠΎΠΉ Π½Π°ΡΠ°Π»ΡΠ½ΠΎΠΉ ΡΠΎΡΠΊΠΈ ΠΊ Π·Π°Π΄Π°Π½Π½ΠΎΠΉ ΠΊΠΎΠ½Π΅ΡΠ½ΠΎΠΉ ΡΠΎΡΠΊΠ΅. ΠΠΎ-Π²ΡΠΎΡΡΡ
, ΡΡΠΎΡ ΠΏΡΡΡ Π΄ΠΎΠ»ΠΆΠ΅Π½ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΠ²Π°ΡΡ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΠ΅ ΡΠΎΠ±ΠΎΡΠ° Ρ ΠΎΠ±Ρ
ΠΎΠ΄ΠΎΠΌ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΡ
ΠΏΡΠ΅ΠΏΡΡΡΡΠ²ΠΈΠΉ. Π-ΡΡΠ΅ΡΡΠΈΡ
, ΠΏΡΡΡ Π΄ΠΎΠ»ΠΆΠ΅Π½ ΡΡΠ΅Π΄ΠΈ Π²ΡΠ΅Ρ
Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΡ
ΠΏΡΡΠ΅ΠΉ, ΡΠ΄ΠΎΠ²Π»Π΅ΡΠ²ΠΎΡΡΡΡΠΈΡ
ΠΏΠ΅ΡΠ²ΡΠΌ Π΄Π²ΡΠΌ ΡΡΠ΅Π±ΠΎΠ²Π°Π½ΠΈΡΠΌ, Π±ΡΡΡ Π² ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΠΌ ΡΠΌΡΡΠ»Π΅ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΡΠΌ.ΠΠ΅ΡΠΎΠ΄Ρ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΡΠΈ ΠΌΠΎΠΆΠ½ΠΎ ΠΊΠ»Π°ΡΡΠΈΡΠΈΡΠΈΡΠΎΠ²Π°ΡΡ ΠΏΠΎ ΡΠ°Π·Π½ΡΠΌ ΠΏΡΠΈΠ·Π½Π°ΠΊΠ°ΠΌ. Π ΠΊΠΎΠ½ΡΠ΅ΠΊΡΡΠ΅ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΈΠ½ΡΠ΅Π»Π»Π΅ΠΊΡΡΠ°Π»ΡΠ½ΡΡ
ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΠΉ ΠΈΡ
ΠΌΠΎΠΆΠ½ΠΎ ΡΠ°Π·Π΄Π΅Π»ΠΈΡΡ Π½Π° ΡΡΠ°Π΄ΠΈΡΠΈΠΎΠ½Π½ΡΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΈ ΡΠ²ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ. ΠΠΎ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΡ ΠΎΠΊΡΡΠΆΠ°ΡΡΠ΅ΠΉ ΠΎΠ±ΡΡΠ°Π½ΠΎΠ²ΠΊΠΈ ΠΌΠΎΠΆΠ½ΠΎ ΡΠ°Π·Π΄Π΅Π»ΠΈΡΡ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π½Π° ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π² ΡΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΎΠΊΡΡΠΆΠ°ΡΡΠ΅ΠΉ ΡΡΠ΅Π΄Π΅ ΠΈ Π² Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΠ΅Π΄Π΅ (ΡΠ»Π΅Π΄ΡΠ΅Ρ, ΠΎΠ΄Π½Π°ΠΊΠΎ, ΠΎΡΠΌΠ΅ΡΠΈΡΡ, ΡΡΠΎ ΡΡΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΎΠΊΡΡΠΆΠ°ΡΡΠ°Ρ ΡΡΠ΅Π΄Π° ΡΠ΅Π΄ΠΊΠΎ Π²ΡΡΡΠ΅ΡΠ°Π΅ΡΡΡ Π½Π° ΠΏΡΠ°ΠΊΡΠΈΠΊΠ΅). ΠΠ΅ΡΠΎΠ΄Ρ ΡΠ°ΠΊΠΆΠ΅ ΠΌΠΎΠΆΠ½ΠΎ ΡΠ°Π·Π΄Π΅Π»ΠΈΡΡ ΠΏΠΎ ΠΏΠΎΠ»Π½ΠΎΡΠ΅ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ ΠΎΠ± ΠΎΠΊΡΡΠΆΠ°ΡΡΠ΅ΠΉ ΡΡΠ΅Π΄Π΅: ΠΌΠ΅ΡΠΎΠ΄Ρ Ρ ΠΏΠΎΠ»Π½ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠ΅ΠΉ (Π² ΡΠ°ΠΊΠΎΠΌ ΡΠ»ΡΡΠ°Π΅ Π³ΠΎΠ²ΠΎΡΡΡ ΠΎ Π³Π»ΠΎΠ±Π°Π»ΡΠ½ΠΎΠΌ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΠΏΡΡΠΈ) ΠΈ ΠΌΠ΅ΡΠΎΠ΄Ρ Ρ Π½Π΅ΠΏΠΎΠ»Π½ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠ΅ΠΉ (ΠΎΠ±ΡΡΠ½ΠΎ ΡΠ΅ΡΡ ΠΈΠ΄Π΅Ρ ΠΎ Π·Π½Π°Π½ΠΈΠΈ ΠΎΠ±ΡΡΠ°Π½ΠΎΠ²ΠΊΠΈ Π² Π½Π΅ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²Π΅Π½Π½ΠΎΠΉ Π±Π»ΠΈΠ·ΠΎΡΡΠΈ ΠΎΡ ΡΠΎΠ±ΠΎΡΠ°, Π² ΡΡΠΎΠΌ ΡΠ»ΡΡΠ°Π΅ ΡΠ΅ΡΡ ΠΈΠ΄Π΅Ρ ΠΎ Π»ΠΎΠΊΠ°Π»ΡΠ½ΠΎΠΌ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΠΏΡΡΠΈ). ΠΡΠΌΠ΅ΡΠΈΠΌ, ΡΡΠΎ Π½Π΅ΠΏΠΎΠ»Π½Π°Ρ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΡ ΠΎΠ± ΠΎΠΊΡΡΠΆΠ°ΡΡΠ΅ΠΉ ΡΡΠ΅Π΄Π΅ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ ΡΠ»Π΅Π΄ΡΡΠ²ΠΈΠ΅ΠΌ ΠΌΠ΅Π½ΡΡΡΠ΅ΠΉΡΡ ΠΎΠ±ΡΡΠ°Π½ΠΎΠ²ΠΊΠΈ, Ρ.Π΅. Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ
Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΠ΅Π΄Ρ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΡΡΠΈ, ΠΊΠ°ΠΊ ΠΏΡΠ°Π²ΠΈΠ»ΠΎ, Π»ΠΎΠΊΠ°Π»ΡΠ½ΠΎΠ΅.Π Π»ΠΈΡΠ΅ΡΠ°ΡΡΡΠ΅ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΎ Π±ΠΎΠ»ΡΡΠΎΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΡΠΈ, Π² ΠΊΠΎΡΠΎΡΡΡ
ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠ΅ ΡΠ²ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΡΠΈΠ΅ΠΌΡ, Π²ΡΡΠ΅ΠΊΠ°ΡΡΠΈΠ΅, ΠΊΠ°ΠΊ ΠΏΡΠ°Π²ΠΈΠ»ΠΎ, ΠΈΠ· ΡΠΎΠ΄Π΅ΡΠΆΠ°ΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠΌΡΡΠ»Π° ΡΠ΅ΡΠ°Π΅ΠΌΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ. Π Π½Π°ΡΡΠΎΡΡΠ΅ΠΌ ΠΎΠ±Π·ΠΎΡΠ΅ Β ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Ρ ΠΊ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ. ΠΠ΄Π΅ΡΡ ΠΌΠΎΠΆΠ½ΠΎ Π²ΡΠ΄Π΅Π»ΠΈΡΡ ΠΏΡΡΡ ΠΊΠ»Π°ΡΡΠΎΠ² ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ²: ΠΌΠ΅ΡΠΎΠ΄Ρ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π³ΡΠ°ΡΠΎΠ², ΠΌΠ΅ΡΠΎΠ΄Ρ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΊΠ»Π΅ΡΠΎΡΠ½ΠΎΠΉ Π΄Π΅ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΈΠΈ, ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΡ
ΠΏΠΎΠ»Π΅ΠΉ, ΠΎΠΏΡΠΈΠΌΠΈΒΠ·Π°ΡΠΈΠΎΠ½Π½ΡΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ, ΠΌΠ΅ΡΠΎΠ΄Ρ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΈΠ½ΡΠ΅Π»Π»Π΅ΠΊΡΡΠ°Π»ΡΠ½ΡΡ
ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΠΉ.ΠΠ½ΠΎΠ³ΠΈΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΡΠΈ Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ° Π΄Π°ΡΡ ΡΠ΅ΠΏΡ ΠΎΠΏΠΎΡΠ½ΡΡ
ΡΠΎΡΠ΅ΠΊ (ΠΏΡΡΠ΅Π²ΡΡ
ΡΠΎΡΠ΅ΠΊ), ΡΠΎΠ΅Π΄ΠΈΠ½ΡΡΡΡΡ Π½Π°ΡΠ°Π»ΠΎ ΠΈ ΠΊΠΎΠ½Π΅Ρ ΠΏΡΡΠΈ. ΠΡΠΎ ΡΠ»Π΅Π΄ΡΠ΅Ρ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡ ΠΊΠ°ΠΊ ΠΏΡΠΎΠΌΠ΅ΠΆΡΡΠΎΡΠ½ΡΠΉ ΡΠ΅Π·ΡΠ»ΡΡΠ°Ρ. ΠΠΎΠ·Π½ΠΈΠΊΠ°Π΅Ρ Π·Π°Π΄Π°ΡΠ° ΠΏΡΠΎΠΊΠ»Π°Π΄ΠΊΠΈ ΠΏΡΡΠΈ Π²Π΄ΠΎΠ»Ρ ΠΏΠΎΡΡΡΠΎΠ΅Π½Π½ΠΎΠΉ ΡΠ΅ΠΏΠΈ ΠΎΠΏΠΎΡΠ½ΡΡ
ΡΠΎΡΠ΅ΠΊ, Π½Π°Π·ΡΠ²Π°Π΅ΠΌΠ°Ρ Π·Π°Π΄Π°ΡΠ΅ΠΉ ΡΠ³Π»Π°ΠΆΠΈΠ²Π°Π½ΠΈΡ ΠΏΡΡΠΈ. ΠΡΠΎΠΉ Π·Π°Π΄Π°ΡΠ΅ Π² ΠΎΠ±Π·ΠΎΡΠ΅ ΡΠ°ΠΊΠΆΠ΅ ΡΠ΄Π΅Π»Π΅Π½ΠΎ Π²Π½ΠΈΠΌΠ°Π½ΠΈΠ΅
Sampling-based Algorithms for Optimal Motion Planning
During the last decade, sampling-based path planning algorithms, such as
Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have
been shown to work well in practice and possess theoretical guarantees such as
probabilistic completeness. However, little effort has been devoted to the
formal analysis of the quality of the solution returned by such algorithms,
e.g., as a function of the number of samples. The purpose of this paper is to
fill this gap, by rigorously analyzing the asymptotic behavior of the cost of
the solution returned by stochastic sampling-based algorithms as the number of
samples increases. A number of negative results are provided, characterizing
existing algorithms, e.g., showing that, under mild technical conditions, the
cost of the solution returned by broadly used sampling-based algorithms
converges almost surely to a non-optimal value. The main contribution of the
paper is the introduction of new algorithms, namely, PRM* and RRT*, which are
provably asymptotically optimal, i.e., such that the cost of the returned
solution converges almost surely to the optimum. Moreover, it is shown that the
computational complexity of the new algorithms is within a constant factor of
that of their probabilistically complete (but not asymptotically optimal)
counterparts. The analysis in this paper hinges on novel connections between
stochastic sampling-based path planning algorithms and the theory of random
geometric graphs.Comment: 76 pages, 26 figures, to appear in International Journal of Robotics
Researc
A generalized laser simulator algorithm for optimal path planning in constraints environment
Path planning plays a vital role in autonomous mobile robot navigation, and it has thus become one of the most studied areas in robotics. Path planning refers to a robot's search for a collision-free and optimal path from a start point to a predefined goal position in a given environment. This research focuses on developing a novel path planning algorithm, called Generalized Laser Simulator (GLS), to solve the path planning problem of mobile robots in a constrained environment. This approach allows finding the path for a mobile robot while avoiding obstacles, searching for a goal, considering some constraints and finding an optimal path during the robot movement in both known and unknown environments. The feasible path is determined between the start and goal positions by generating a wave of points in all directions towards the goal point with adhering to constraints. A simulation study employing the proposed approach is applied to the grid map settings to determine a collision-free path from the start to goal positions. First, the grid mapping of the robot's workspace environment is constructed, and then the borders of the workspace environment are detected based on the new proposed function. This function guides the robot to move toward the desired goal. Two concepts have been implemented to find the best candidate point to move next: minimum distance to goal and maximum index distance to the boundary, integrated by negative probability to sort out the most preferred point for the robot trajectory determination. In order to construct an optimal collision-free path, an optimization step was included to find out the minimum distance within the candidate points that have been determined by GLS while adhering to particular constraint's rules and avoiding obstacles. The proposed algorithm will switch its working pattern based on the goal minimum and boundary maximum index distances. For static obstacle avoidance, the boundaries of the obstacle(s) are considered borders of the environment. However, the algorithm detects obstacles as a new border in dynamic obstacles once it occurs in front of the GLS waves. The proposed method has been tested in several test environments with different degrees of complexity. Twenty different arbitrary environments are categorized into four: Simple, complex, narrow, and maze, with five test environments in each. The results demonstrated that the proposed method could generate an optimal collision-free path. Moreover, the proposed algorithm result are compared to some common algorithms such as the A* algorithm, Probabilistic Road Map, RRT, Bi-directional RRT, and Laser Simulator algorithm to demonstrate its effectiveness. The suggested algorithm outperforms the competition in terms of improving path cost, smoothness, and search time. A statistical test was used to demonstrate the efficiency of the proposed algorithm over the compared methods. The GLS is 7.8 and 5.5 times faster than A* and LS, respectively, generating a path 1.2 and 1.5 times shorter than A* and LS. The mean value of the path cost achieved by the proposed approach is 4% and 15% lower than PRM and RRT, respectively. The mean path cost generated by the LS algorithm, on the other hand, is 14% higher than that generated by the PRM. Finally, to verify the performance of the developed method for generating a collision-free path, experimental studies were carried out using an existing WMR platform in labs and roads. The experimental work investigates complete autonomous WMR path planning in the lab and road environments using live video streaming. The local maps were built using data from live video streaming s by real-time image processing to detect the segments of the lab and road environments. The image processing includes several operations to apply GLS on the prepared local map. The proposed algorithm generates the path within the prepared local map to find the path between start-to-goal positions to avoid obstacles and adhere to constraints. The experimental test shows that the proposed method can generate the shortest path and best smooth trajectory from start to goal points in comparison with the laser simulator