Maintaining multi-level planar maps in intelligent systems

We present algorithms that allow an intelligent system to dynamically convert between two representations of spatial occupancy, namely, certainty grids and object boundary curves. These algorithms can be used to accomplish many real-time tasks of a mobile robot such as mapping, navigation, object recognition, and robot localization. For conversion from certainty grid to object boundaries, an edge linking algorithm [8] is appropriately modified. Certainty grid ‘images’ are transformed into a set of object boundary curves. The latter are expressed as oriented piecewise linear segments. Image processing techniques, such as edge detection, thinning, curve tracing, and linear approximation are employed with various modifications. Modifications include a new method for linear curve approximation that is simple, accurate, and efficient. This method monitors chord and arc length and its excellent performance is demonstrated against similar algorithms. The certainty grid to object boundary algorithm is tested against simulated noisy certainty grid maps. An algorithm to do the inverse operation, namely, to convert object boundary curves to an occupancy grid, is also presented. 1 I n t r o d u c t i o n An intelligent system contains world model representations of entities necessary for the accomplishment of its goals. For example, a mobile robot must represent (implicitly or explicitly) the obstacles in its environment. Researchers have often chosen a single type of representation for all entities. We argue the utility of multiple representations of the same entity. The main objection to having multiple representations of the same entity in a real-time system is the problem of maintaining consistency between the representations. This problem is avoided when real-time conversion algorithms are defined and used. We present two such algorithms in this paper. With processor and memory costs continuing to fall and the availability of parallel bus architectures, maintaining multiple representation types in real-time intelligent systems is becoming more feasible. The system benefits by being able to choose the representation most appropriate for the accomplishment of each task. Two useful and complementary map representations are certainty grids [7] and object boundary curves. They are particularly useful for mobile robot control. For example, vectors normal to an object boundary would be difficult to get from a certainty grid, but relatively easy to obtain from an object boundary curve. Spatial occupancy information is gotten easily from certainty grids but not as easily from object boundary curves. Additionally, representing spatial occupancy in the form of object boundary curves is important for the detection of higher level features such as corners, curves, and lines. As a result, high level geometric features can be more easily computed, perceived, and updated and, for example, can be used by the mobile robot to reorient itself or to recognize objects. It is relatively easy to build and maintain a certainty grid which makes it a good local map. However, a certainty grid representation for a global map may require a forbidding amount of storage space, whereas, an object boundary curve representation is more compact without sacrificing accuracy or utility. Since we seek to maintain these two particular representations of a dynamic occupancy map in real-time intelligent systems, we need real-time map conversion algorithms. We have developed two algorithms to do this real-time conversion, namely, certainty grid to object boundary (CGOB) and object boundary to occupancy grid (OBOG). Our claim of real-time performance is two-fold, 1) both algorithms are O(n) where n is the number of pixels in the object boundary curves and 2) if the image processing segments of the algorithms are done on each pixel in parallel, the CGOB can execute in roughly five seconds or less for a standard sized image (i.e., 256 pixels) on standard computing hardware. The OBOG algorithm executes much faster than CGOB. These numbers have been determined experimentally. Significant speed ups can be made on this prototype code. The CGOB algorithm we have developed has been tested against simulated certainty grids of various types corrupted by blurring and speckle noise (figure 6). The object boundary curve points encode (in the ordering of those points) which side of the curve is occupied. The CGOB algorithm concludes with a piecewise linear curve approximation algorithm. The popular split and merge approach [6, 5] is known to be inefficient and several attempts to improve its efficiency come with an increase in complexity [8, 11]. We have developed a new approach that is accurate, simple, and efficient. We compare this new approach to some others in the literature. The OBOG algorithm has been tested against object boundary curves of various types (figures 9 and 10). This algorithm is significantly simpler than the CGOB algorithm and can also be computed in parallel on a pixel processor. 2 M u l t i l e v e l r e p r e s e n t a t i o n s i n a n i n t e l l i g e n t s y s t e m Hierarchical intelligent control, as described in [1], specifies a real-time, multi-level interaction of prediction and error formation. The certainty grid representation allows prediction of points (low level), whereas the object boundary representation allows prediction of lines and shapes (higher level). The CGOB and OBOG algorithms will allow both representations to simultaneously exist and be updated in a real-time hierarchical intelligent control system in a manner illustrated in figure 1. For example, robot range and position data can be used to update a certainty grid (a ‘point’ type of representation). Using CGOB, we convert this map to a set of object boundaries which can be considered to be a ‘higher’ level representation since we have now aggregated point features into linear features. These object boundary curves are then stored in the world model and can be used, for example, to do object recognition. Object recognition can be used to generate a more precise boundary map and OBOG can be used to create occupancy grid estimates. Knowledge of commanded motions can also contribute to better estimates. 3 T h e c e r t a i n t y g r i d t o o b j e c t b o u n d a r y a l g o r i t h m We now describe the CGOB algorithm: 1) Create a raw edge grid using two orthogonal 5x5 gradient operators on a noisy certainty grid. 2) Threshold and thin the raw edge grid and use this result to compute arrays of 'predecessors' and 'successors' . 3) Group contiguous cells in the thinned edge grid, constituting contiguous edge cells. 4) Do local Gaussian smoothing on each group of points (to filter quantization noise). 5) Approximate the smoothed boundary points with contiguous line segments by monitoring change in chord length and path length. 3 . 1 E d g e de t e c t i o n We used two 5x5 orthogonal stochastic gradient operators [6] for computing the gradient. 3x3 operators didn’t produce smooth thinned edges, so 5x5 operators were required. Stochastic gradient operators have the advantage of performance tailored to the expected signal to noise characteristics of the raw certainty grid. This signal to noise ratio (SNR) needs to be computed from a representative noisy certainty grid in order to be accurate. We performed our simulations with a somewhat low SNR of one. Certainty grid map to object boundary map conversion algorithm (CGOB) Certainty grid map update algorithm Certainty grid map prediction algorithm range data robot position and orientation data Current occupancy grid estimate Sensed certainty grid Sensed object boundary curves Predicted object boundary curves Sensed certainty grid Predicted occupancy grid Object boundary map to occupancy grid map conversion algorithm (OBOG) commanded robot motion commanded robot motion SP1 SP2 LEVEL 1: POINTS LEVEL 2: LINEAR FEATURES