Exploiting Critical Points to Reduce Positioning Error for Sensor-Based Navigation

-This p a p e r p r e s e n t s a p l a n n e r t h a t d e t e r m i n e s a p a t h s u c h t h a t t h e r o b o t d o e s n o t h a v e t o h e a v i l y r e l y o n o d o m e t r y t o r e a c h i ts goa l . T h e p l a n n e r d e t e r m i n e s a s e q u e n c e o f o b s t a c l e b o u n d a r i e s t h a t t h e r o b o t m u s t fo l low t o r e a c h t h e goa l . S ince t h i s p l a n n e r is u s e d in t h e c o n t e x t o f a c o v e r a g e a l g o r i t h m a l r e a d y p r e s e n t ed b y t h e a u t h o r s ~ we a s s u m e t h a t t h e f r ee s p a c e is a lready~ c o m p l e t e l y o r pa r t i a l ly~ r e p r e s e n t e d b y a ce l lu l a r d e c o m p o s i t i o n w h o s e cell b o u n d a r i e s a r e d e f i n e d by c r i t i c a l p o i n t s o f M o r s e f u n c t i o n s ( i s o l a t e d p o i n t s a t ob s t a c l e b o u n d a r i e s ) . T h e t o p o l o g i c a l r e l a t i o n s h i p a m o n g t h e cel ls is r e p r e s e n t e d b y a g r a p h w h e r e n o d e s a r e t h e c r i t i c a l p o i n t s a n d e d g e s c o n n e c t t h e n o d e s t h a t de f i ne a c o m m o n cell (i.e.~ t h e e d g e s c o r r e s p o n d t o t h e cel ls t h e m s e l v e s ) . A s e a r c h o f t h i s g r a p h y i e l d s a s e q u e n c e o f cel ls t h a t d i r e c t s t h e r o b o t f r o m a s t a r t t o a goa l . O n c e a s e q u e n c e o f cel ls a n d c r i t i c a l p o i n t s a r e d e t e r mined~ a r o b o t t r a v e r s e s e a c h cell b y m a i n l y f o l l o w i n g t h e b o u n d a r y o f t h e cell a l o n g t h e o b s t a c l e b o u n d a r i e s a n d m i n i m i z e s t h e a c c u m u l a t e d d e a d r e c k o n i n g e r r o r a t t h e i n t e r m e d i a t e c r i t i c a l p o i n t s . T h i s a l l o w s t h e r o b o t t o r e a c h t h e g o a l r o b u s t l y e v e n in t h e p r e s e n c e o f d e a d r e c k o n i n g e r r o r . Keywords--Navigat ion, t o p o l o g i c a l l o c a l i z a t i o n , c r i t i ca l p o i n t s . 1 I n t r o d u c t i o n Classical motion planning techniques [10] have successfully supplied algorithms that determine a path between start and goal configurations assuming perfect position information is available. Three methods have dominated the motion planning field: start-goal planners [11], [15], roadmaps [3], and exact or approximate cellular decompositions [4], [17]. This work exploits the structure of an exact cellular decomposition to plan a path between start and goal configurations that is less "sensitive" to dead-reckoning error. Exact cellular decompositions represent the free space as the union of non-overlapping regions called cells such that adjacent cells share a common boundary. Our work is mainly motivated by earlier work in covering unknown spaces using cellular decompositions [1]. The details of how to use a cellular decomposition to perform coverage is not pertinent to this paper. However, when incrementally constructing a cellular decomposition, the planner must use a start-goal planner to direct the robot from one cell to another. In this paper, we address the start-to-goal path planning problem from a localization perspective without heavily relying absolute position of the mobile robot determined using odometry which is prone to accrue error. We assume that the robot navigates through a free space that has been partially mapped or mapped via a cellular decomposition. Using this cellular decomposition, we develop a navigation algorithm as a first step towards automatically defining topologically meaningful natural landmarks and connections between them which the robot can use to robustly navigate from one point to another. We used critical points (points on obstacle boundaries) where a topological change in the space occurs to define cells that have "simple" structure of nonintersecting "upper"and "lower" boundaries without critical points on them, and side boundaries that contain critical points (Fig. 1). When the planner determines a path, i.e., a sequence of cells, it has determined a topological path, not an exact one. The planner then determines the exact path by following the upper or lower boundary of each cell, possibly switching from an upper to a lower (or visa versa) at a critical point. Most of this path is robust to odometry error because the robot servos off of the boundary most of the time, only departing this "safe" area at some of the critical points. This method strikes resonance with probabilistic method of Roy et al. [16] which they term a coastal navigation approach. This approach directs the robot to remain close to obstacle boundaries which increases the chances of gathering information for localization. The philosophy of utilizing topological information to position a robot is based on our previous work in simultaneous mapping and localization algorithms without explicit localization using the topology of generalized Voronoi diagrams (set of points equidistant to two obstacles) [6]. We used the nodes of the diagram as the topological features of the free space to localize. This method was based on Kuipers [9] that utilizes distinctive places for mobile robot navigation. It is also worth pointing out the work of Dudeck et al. [7] who also uses a topological method for localization.