ARTIGO TÉCNICO Lounis Adouane LASMEA, UBP-UMR CNRS 6602, France email@example.com
ORBITAL OBSTACLE AVOIDANCE ALGORITHM FOR RELIABLE AND ON-LINE MOBILE ROBOT NAVIGATION ABSTRACT This paper proposes an orbital obstacle avoidance algorithm which permits to obtain safe and smooth robot navigation in very cluttered environments. This algorithm uses speciﬁc reference frame which gives accurate indication on robot situation. The robot knows thus if it must avoid the obstacle in clockwise or counter-clockwise direction. Moreover, it knows the moment to go into the orbit of the obstacle and the moment to go out. These orbital behaviors are performed using adaptive limit-cycle trajectories. The later with a speciﬁc conﬂicting situations module permit to prevent robot oscillations, local minima and dead ends. The proposed algorithm is embedded in a speciﬁc bottom-up control architecture with stability proof given according to Lyapunov synthesis. The overall proposed structure of control allows to decrease signiﬁcantly the time to reach the target. In fact, according to the proposed algorithm, robot anticipates the collisions with obstacles according to smooth local trajectory modiﬁcations. A large number of simulations in different environments are performed to demonstrate the efﬁciency and the reliability of the proposed control architecture.
I. INTRODUCTION Obstacle avoidance controllers have a predominating function to achieve autonomously and safely the navigation of mobile robots in cluttered and unstructured environments. Khatib in  proposes a real-time obstacle avoidance approach based on the principle of artiﬁcial potential ﬁelds. He assumes that the robot actions are guided by the sum of attractive and repulsive ﬁelds. Arkin in  extends Khatib’s approach while proposing speciﬁc schema motors for mobile robots navigation. Nevertheless, these methods suffer from the local minima problem when for instance, the sum of local gradient is null. In , Elnagar et al., propose to model the repulsive potential ﬁeld characterizing obstacles by Maxwell’s equations which have the merit to completely eliminate the local minima problem. Fuzzy control is widely used to perform robust obstacle avoidance , . This formalism allows to integrate several linguistic rules to avoid dead ends or local minima . Unfortunately, its lacks of stability demonstration of the applied control laws. Another interesting approach, based on a reﬂex behavior reaction, uses the Deformable Virtual Zone (DVZ) concept, in which a robot kinematic dependent risk zone surrounds the robot . If an obstacle is detected, it will deform the DVZ and the approach consists to minimize this deformation by modifying the control vector. An interesting overview of other obstacle avoidance methods is accurately given in . Nevertheless, the obstacle avoidance controller is only a part of the different functions which must constitute an overall control architecture for navigation tasks. One part of the literature in this domain considers that the robot is fully actuated with no control bound and focuses the attention on path planning. Voronoï diagrams and visibility graphs  or navigation functions  are among these roadmap-based methods. However, the other part of the literature considers that to control a robot with safety, ﬂexibility and reliability, it is essential to accurately take into account: robot’s structural constraints (e.g., nonholonomy); avoid command discontinuities and set-point jerk, etc. Nevertheless, even in this method, there are two schools of thought, one uses the notion of planning and re-planning to reach the target, e.g.,  and  and the other more reactive (without planning) like in ,  or . Our proposed control architecture is linked to this last approach. Therefore, where the stability of robot control is rigourously demonstrated and the overall
robot behavior is constructed with modular and bottom-up approach . The proposed on-line obstacle avoidance algorithm uses speciﬁc orbital trajectories given by limit-cycle differential equations , . The proofs of controllers stability are given using Lyapunov functions. The proposed algorithm provides also several mechanisms to prevent oscillations, local minima and dead end robot situations. The rest of the paper is organized as follows. Section II gives the speciﬁcation of the task to achieve. The details of the proposed control architecture are given in section III. It presents the model of the considered robot and the implemented elementary controllers laws. Section IV gives in details the proposed obstacle avoidance algorithm whereas section V introduces the conﬂicting situations management module. Section VI is devoted to the description and analysis of simulation results. This paper ends with some conclusions and further work.
II. NAVIGATION IN PRESENCE OF OBSTACLES The objective of the navigation task in an unstructured environment is to lead the robot towards one target while avoiding statical and dynamical obstacles. One supposes in the setup that obstacles and the robot are surrounded by bounding cylindrical boxes with respectively 52 and 55 radii . The target to reach is also characterized by a circle of 57 radius. Several perceptions are also necessary for the robot navigation (cf. Figure 1):
Figure 1 . The used perceptions for mobile robot navigation
ments proves the efﬁciency and the ﬂexibility of the control. The proposed algorithm allows also to reduce the time needed to reach the target. In fact, according to this algorithm, robot anticipates the collisions with obstacles according to smooth local trajectory modiﬁcations. Future work will ﬁrst test the proposed control architecture on the CyCab vehicle . The second step is to adapt the proposed structure of control to more complex tasks like the navigation in highly dynamical environment.
REFERENCES Figure 10 . Evolution of Lyapunov functions for the two used controllers
Figure 11 . Smooth trajectory obtained with the proposed orbital algorithm
VII. CONCLUSION AND FURTHER WORK In this paper, an obstacle avoidance algorithm based on orbital limit-cycle trajectories is proposed. This algorithm was embedded in an on-line behavioral control architecture and permits for a mobile robot to navigate in cluttered environments with safe and reliable way. In addition to the use of limitcycles, the algorithm uses speciﬁc reactive rules which allows to the robot to avoid deadlocks, local minima and oscillations. These simple rules are efﬁcient and permits to the proposed algorithm to do not becomes more and more complex. In other terms, the proposed control structure is open and ﬂexible in the sense that it can manage a lot of other conﬂicts situations while only adding simple reactive rules. Otherwise, the stability proof of the overall control architecture is given. Statistical survey in different environ-
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