Economical and Cautious Approaches to Local PathPlanning for a Mobile Robot

P. Grant and P. H. Mowforth

The Turing Institute, 36 North Hanover St., Glasgow Gl 2AD, Scotlandtel: +41-552-6400, fax: +41-552-4245, e-mail {paul,boffin}@turing.ac.uk

This paper describes a mobile robot projectwhich couples both a vision system and a plan-ning system. In particular, we describe how a worldmodel is constructed in the vision system, and howthis is utilised in the generation of a point-to-pointpath for the robot. We show, that through similartechniques, two qualitatively differing plans may begenerated - namely the economical path, and thecautious path.

Most mobile robotic systems can be decomposedinto a number of sub-systems, each performing aclearly defined task but with the overall goal ofgearing perception to action. Figure 1 shows a pic-ture of one of the Turing Institutes mobile robots,called Turnip 1, whilst Figure 2 illustrates thesesub-systems.

A clear distinction exists between a world knowl-edge base and a world model. The former codes ab-stract relational information concerning the worldin a form which allows a) recognition, b) inference,or c) global planning. The latter codes geometricinformation concerning the world in a form whichallows a) sensor fusion, b) obstacle avoidance or c)local planning. Whilst a world knowledge base maybe learned or predefined, the world model providesa buffered summary of our immediated perceptions.

Planning may be further refined into global plan-ning and local planning. Global planning is con-cerned with the generation of an ordered sequenceof sub-goals culminating in the achievement of a re-quired task. For navigation, these will typically bea list of landmarks connected by goto commands.Local planning is concerned with the generationof a point-to-point path between these landmarks.Whilst global planning utilises the world knowledgebase, local planning requires sensory informationobtained via the world model.

Figure 1: One of the Turnip 1 mobile robot proto-types in the Turing Institute.

This paper outlines an approach for the construc-tion of a world model and, more specifically, howthis may be utilised in the generation of a local plan.

1 Generating a world model

The Turnip 1 mobile features two forward facingcameras. The images are used as a basis for com-puting intrinsic scene information using stereo andmotion data. The image matching is carried outusing a Multiple Scale Signal Matching algorithm,MSSM[3], which provides smooth continuous so-lutions in the matched output. The algorithm

297AVC 1989 doi:10.5244/C.3.53

Worldmodel

Figure 2: Major software subsystems of the mobilerobot.

has several similarities to that described by Anan-dan [1]. Figure 3 shows the outputs of the signalmatcher expressed as p,q and d maps. The p andq maps express the horizontal and vertical distor-tions respectively between successive frames fromeach camera whilst the d maps express the disparityinformation between stereo pairs of images. In thisway, the p,q and d maps allow every visible patchof surface to be tracked smoothly and continuouslyin both time and space.

With each new frame, a new world model is con-structed as a 3D voxel occupancy grid. As datafusion has already been achieved, there is no needto express probabilities in the structure. The occu-pancy grid, called TOspace, is a three state modelfor which voxels are labelled as Transparent (freespace), Opaque (solid surfaces) or unknown (oc-cluded). The model uses the natural scaling offeredby the signal matching results. As such, using onlyone scale, it uses a robot-centered, elastically de-formed magnification bubble in which the world isexpressed with ever coarser resolution away fromthe robot out to effective infinity. In order to pre-serve surface data described at other points in timeand space, it is necessary to use a model which over-samples, i.e. hyper-resolution. At present, the vi-sual short-term memory for the model uses only thelast three frames.

For further details of the TOspace world modelsee Shapiro and Mowforth (in preparation).

2 Local planning

TOspace offers a useful framework for earring outlocal planning. As the model is continuously beingrebuilt after each perception cycle, all the potentialobstacles in the environment are labelled.

Within the local environment of the robot, fol-

Left Image movie

TOipaceworld model

Ri|ktinugc movie

Figure 3: Overview of the robot vision system fromthe cameras to the world model.

lowing each perception cycle, the model is used togenerate a proximity description at each voxel. Thetask is achieved using the distance transform [2].This simple operation labels voxels with gray-levelswhose values correspond directly to the distancefrom surfaces. The distance transformed worldmodel is termed proximity space.

When deciding what constitutes a good localplan, a spectrum of optimality exists. However,two common criteria for optimality are the path ofshortest distance (an economical route) or the pathof most avoidance (a cautious route).

2.1 Generating an Economical Route

The economical route generation involves a fourstage computation:

1. Generate proximity space with respect to ob-stacles.

2. Threshold to eliminate robot geometry (config-uration space).

3. Generate proximity space with respect to therobot start position.

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1. Original Image 2. Proximity Space wrt Objects

3. Enlarged Objects 4. Proximity Space wrt Robot

5. Generated Plan from Start to Goal

Figure 4: Stages in Generating Shortest Path fromLocation (70, 70) to (7, 60)

4. Generate path of steepest decent from goal tostart.

The first two stages have the effect of enlarg-ing obstacle size whilst reducing robot size accord-ingly (down to unit voxel). Stage 3 uses the dis-tance transform to form a proximity space modelwhere non-feature points have assumed a value de-noting their distance from the robots start (cur-rent) position. Feature points are given a writeprotection, resulting in a refraction around the en-larged obstacles. Stage 4 extracts the route fromstart to goal. Working back from the goal loca-tion, an 8-neighbour search is performed. The min-imum valued voxel (ie. that which is closest to therobots start position) is selected as the next pathvoxel. This process is iterated until the start voxelis reached.

Figure 4 illustrates the process on a 2D scene.

2.2 Generating a Cautious Route

The cautious route generation involves a five stagecomputation:

1. Generate proximity space with respect to ob-stacles.

2. Extract points of local maxima.

3. Generate routes from start and goal location toclosest point of local maxima.

4. Extract connectivity information from result.

5. Use a search to generate a plan through localmaxima.

Stage 1 is exactly as described in the previouscase. Stage 2 is performed by scanning the im-age and checking orthogonal/diagonal voxel pairs.Points of local maxima occur where a point isequidistant from two or more feature points on dif-ferent obstacles. These points are extracted by thefollowing simple classification:

local max iff:(current-voxel > voxell) and (current-voxel > =

voxel2)or

(current-voxel >= voxell) and (current-voxel >voxel2)

This results in the generation of line segmentspassing between obstacles. However, points of localmaxima occur due to the non-convex nature of anobstacle. This may be due to rotation, noise, or theobjects themselves (eg. having a corner). A post-processing step is the removal of such line segments,since traversal along one of these would result in acollision with an obstacle.

Since it is unlikely the start and goal locationswill be a point of local maxima, stage 3 generatesa path between the start (or goal) and the closestpoint line segment. This is achieved through exactlythe same algorithm as generating the economicalpath.

Stage 4 extracts topological information from theresult. This then forms input to a planner, whichperforms a search to generate those line segmentsto be traversed.

Figure 5 illustrates the process on a 2D scene.

It is worth noting that the generation of localroute plans does not require absolute linear scal-

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1. Original Image 2. Proximity Space wrt Objects

3. Local Maxima 4. Cleaned Image

5. Classified Points 6. Generated Plan from Start to GoalFigure 5: Stages in generating clearest path fromlocation (70, 70) to (7, 60)

Start TransparentX region

unknownregion

ing of the world model. For most practical situa-tions, a non-linear scaling (as found in the TOspacemodel) is sufficient in order to navigate to knownlocations. Figure 6 shows a horizontal slice throughthe TOspace model of the corridor as shown in fig-ure 3. The side walls of the corridor get closer (dis-parity reduces) away from the viewpoint. The slicecontains an overlay of two local plans generated us-ing the model.

Acknowlegements: this work has been sup-ported by the Turing Institute, Hunting Engineer-ing Ltd and The National Engineering Laboratory.

Figure 6: A horizontal slice through a TOspaceworld model taken in the corridor with overlays fora cautious (a) and an economical (b) local routeplan.

References

[1] P. Anandan. A computational framework andan algorithm for the measurement of visual mo-tion. International Journal of Computer Vision,2:283-310, 1989.

[2] G. Borgefors. Distance transforms in digitalimages. Computer Vision Graphics and ImageProcessing, 34(3):344-371, 1986.

[3] Z. P. Jin and P. H. Mowforth. A dis-crete approach to signal matching. Researchmemo TIRM-89-036, The Turing Institute,Glasgow, Scotland, January 1989.

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