Providing Haptic Hints to Automatic Motion Planners

Transcription

1 Providing Haptic Hints to Automatic Motion Planners Nancy M. Amato O. Burchan Bayazit Kyunghwan Kim Wookho Son Guang Song Technical Report Department of Computer Science Texas A&M University November 24, 1998 (Revised February 8, 1999) Abstract In this paper, we investigate various paradigms for enabling a human operator and an automatic motion planner to cooperatively solve a motion planning query. Our work is motivated by our experience that automatic motion planners sometimes fail due to the difficulty of discovering critical configurations of the robot that are often naturally apparent to a human observer. In particular, we study how haptic and visual interfaces can be used to enable a user and an automatic motion planner to cooperatively solve a motion planning query. While much progress has been made in the areas of automatic motion planning and haptic interfaces, little attention has been directed towards combining the two. Our goal is to develop cooperation paradigms that are natural for the human operator and beneficial to the automatic planner. Some of the issued addressed in our study include determining natural ways for the user to understand the progress made by the motion planner (e.g., visualization techniques) and developing techniques by which the automatic planner can utilize (easily generated) user-input. In this paper, we propose several possible approaches to these problems, compare them according to ease of use and effectiveness for solving motion planning queries, and provide recommendations for further development. This research supported in part by NSF CAREER Award CCR (with REU Supplement), NSF Grants IIS (with REU Supplement), EIA , and EIA-98937, and by the Texas Higher Education Coordinating Board under grant ARP Bayazit is supported in part by the Turkish Ministry of Education.

2 Physical Environment Interface Virtual Environment visual feedback Visual Display position Motion Planner Human position + force position position + force position + force Haptic Device position + force Dynamic Model Figure 1: VE System Architecture 1 Introduction Motion planning arises in many application domains such as robotics, virtual reality systems, and computeraided design. Algorithms for performing fully automatic motion planning would be highly desirable for many of these applications, and as such, have been the object of much research [11, 17]. Despite the large effort that has been spent on this problem, efficient fully automatic solutions are known only for very limited scenarios. Indeed, there is strong evidence that any complete planner (one that is guaranteed to find a solution or determine that none exists) requires time exponential in the number of degrees of freedom (dof) of the robot [22]. Recently, some promising randomized methods have been proposed (see, e.g., [4, 16]). Nonetheless, despite the great amount of effort spent on motion planning [17], there exist many important applications that have resisted automatic solution. We believe that some such problems might be solved by using user-input to help guide automatic motion planning algorithms. This belief is based on our experience that automatic motion planners sometimes fail due to the difficulty of discovering critical configurations of the robot that are in tight, or crowded, regions of the robot s configuration space but which are crucial configurations in the resulting path. In contrast, such critical configurations are sometimes naturally apparent to a human observer (see, e.g., [2]). On the other hand, automatic methods are very good at computations that human operators find cumbersome and/or overly time consuming, e.g., detailed computations necessary to fully determine a continuous path. 1.1 Our Study In this work, we concentrate on designing a framework for incorporating the strengths of both a human operator and an automatic planning method. In particular, we investigate how haptic and visual interfaces can be used to enable a user and an automatic motion planner to cooperatively solve a motion planning query. Haptic interfaces enable the user to feel and naturally manipulate the virtual objects by estimating the forces generated by the user s contact with the virtual objects and generating the contact force to be delivered to the user via the haptic device. While much progress has been made in the areas of automatic motion planning and haptic interfaces, little attention has been directed towards combining the two. Advances in this area will have important applications in many areas in addition to motion planning, e.g., in augmented reality training systems where a motion planner and an employee could work together to train the worker to perform complex tasks. This paper reports on a study aimed at developing a theoretical framework and practical guidelines for allowing a human operator to work with an automatic planning system using haptic and visual interfaces. The overall architecture of our VE system is shown in Figure 1; the incorporation of a motion planner is a novel feature of our system. In general, we consider a system in which the human operator communicates with the automatic planner by manipulating virtual objects using the haptic interface, capturing (some) configurations of the objects, and passing them to the planner. The planner s progress is communicated to the operator using a visual overlay on the virtual scene. 1

3 Our main goal is to develop cooperation paradigms that are natural for the human operator and beneficial to the automatic planner. This latter necessitates an understanding of and a methodology for exploiting the relative strengths of both the human user and automatic planners. Some of the issues we study include: What are natural ways for the user to understand the progress made by the motion planner (e.g., visualization techniques)? What kind of (easily generated) user input is most useful for the motion planner? How can the motion planner best utilize the user-generated input? In this paper, we propose several possible approaches to the above questions, compare them according to ease of use and effectiveness for solving motion planning queries, and provide recommendations for further development. 2 Our Prototype VE System Our prototype system consisted of a PHANToM haptic device [18] and an SGI O2 graphics workstation. The PHANToM [18] cannot exert moments since although the finger tip has 6 dof, it has only 3 dof for exerting forces. A bilateral connection exists between the PHANToM and the SGI O2 (the graphics display). The graphics keep track of the position updates of the PHANToM finger tip (gimbal), and the PHANToM generates force-feedback using the collision/penetration information from the graphics display. Our hapticinteraction applications were developed using the C++ General Haptic Open Software Toolkit (GHOST SDK) [23]. The operator can use the PHANToM to manipulate a single rigid object in the virtual scene. Two modes of maneuvering were available. In push mode, the operator may lose contact with the object during the manipulation, while in pull mode the operator maintains a fixed point of contact with it. As our study focussed on evaluating various cooperation paradigms, our system incorporates only rudimentary dynamics, collision detection methods, and visual display. Nevertheless, it is sufficiently complex that we encounter many of the key technical challenges involved in providing realistic feedback to the user in a timely fashion. 2.1 Probabilistic Roadmap Methods The automatic planning method used in our system is the obstacle-based probabilistic roadmap method (OBPRM) [3], which is a representative of the class of planners known as probabilistic roadmap methods (PRMs)[1,3,7,9,,14,15,16,20,21].Briefly,PRMs, use randomization (usually during preprocessing) to construct a graph in C-space (a roadmap [17]). Roadmap nodes correspond to collision-free configurations of the robot. Two nodes are connected by an edge if a path between the two corresponding configurations can be found by a local planning method. Queries are processed by connecting the initial and goal configurations to the roadmap, and then finding a path in the roadmap between these two connection points. We believe PRMs are good prospects for haptic interaction due to their need of improvement in crowded environments and because they are amenable to incremental construction. For example, operators could use haptic interfaces to select configurations to be included in the roadmap or to connect different connected components of the roadmap by hand. These ideas are discussed in more detail in Section 4. 3 Human/Planner Communication In this section we describe various mechanisms for the operator to send information to the planner, and for the planner to communicate its progress to the user. While haptic devices have been used in some limited 2

4 situations to generate robot trajectories (see, e.g., [5, 6, 8, 12, 13, 19, 24, 25]), we believe they have great potential for use in truly cooperative systems involving human operators and more general automatic planners. In particular, they could enable the operator to explore the robot s C-space by touch and may therefore provide a bridge between the workspace (understandable to human operators) and C-space (where most planners work). For example, the operator could explore a robot s six-dimensional C-space by combining visualization of the three-dimensional workspace (3 dof for the operator) and force feedback (another 3 dof). The challenge is to determine natural and effective mechanisms for allowing this interaction to occur via the VE s visual and haptic interfaces. Capturing configurations. The human operator communicates with the automatic planner by manipulating virtual objects using the visual and/or haptic interfaces, capturing (some) configurations of the objects, and passing them to the planner. The operator s goal is to discover configurations that will be useful to the planner. Note that this mechanism can also be used for query specification. Displaying configurations. Since most motion planners work in C-space, it would be useful for the operator to represent C-space configurations on the visual display of the workspace. Unfortunately, if many configurations must be displayed simultaneously (e.g., a roadmap), the naive method of simply displaying a configuration would create a scene as difficult to understand as a high-dimensional configuration space. Thus, what is needed are methods of projecting configurations into the workspace. In particular, we represent robot configurations by one (or a few) point(s) in the workspace. For example, when the robot is a single rigid object, we use the positional coordinates of a reference point on the robot s local frame of reference. For flexible or articulated objects, one could represent a configuration by a set of points, one for each body in the linkage. The robot configuration of a specific projection could be displayed to the operator when he/she clicks on the projection, or when the haptic device is in the vicinity of it. These last two methods have not yet been implemented in our system. Displaying paths/roadmaps. Once the projection from C-space to workspace is defined, connections between configurations can be displayed as edges between the projected sets. Since multiple configurations can project to the same workspace representation (unavoidable as we are projecting from an at least 6- dimensional space into a 3-dimensional space), we use colored edges to differentiate different path fragments or roadmap components. For large roadmaps, the simultaneous projection of all connections (roadmap edges) would be confusing to the operator. In this case, a representative set of the connections of each connected component is portrayed. For example, for each connected component, we display only as many edges as are needed to illustrate its connectivity (and in fact, these edges are not necessarily present in the roadmap). (See, e.g., Figure 3.) Similarly, a representative sample of configurations could be obtained by displaying a fixed number of configurations that are furthest from the center of mass (in the workspace) of all the configurations in the component, or statistical sampling could be used to select configurations with the highest variance from the mean. These methods of selecting samples of configurations have not yet been implemented in our system. 4 Human/Planner Cooperation As mentioned in Section 1, we believe that hints from human operators could provide a means of increasing the efficiency of automatic methods, while still relieving the operator from the tedious, time-consuming work of producing the path manually. In this section we describe several general ways in which the human operator and the motion planner can work together to solve a motion planning query. In Section 5, we compare these methods according to ease of use and effectiveness for solving motion planning queries. 3

5 C-Space Obstacle surface configurations generated from approximate path approximate path generated by operator C-Space Obstacle Workspace Obstacle approximate path generated by operator c l surface configurations generated from approximate path d4 robot c f new segment replacing colliding segment c f new segment replacing colliding segment c l d2 d3 d1 closest translation direction for a robot configuration (a) (b) (c) Figure 2: Pushing approximate paths to free space: (a) simple push (k =1), (b) shortest push, (c) workspace assisted push. 4.1 The Operator s Role The operator s role is to capture configurations that will be useful for the planner. For example, the operator could help the planner by viewing the workspace representation of the evolving roadmap, and capturing paths or configurations that will enable the planner to connect different roadmap components. We implemented two modes of configuration generation: paths: the operator generates sequences of configurations, and critical configurations: the operator generates only selected configurations thought to be essential for the query. A potential advantage of collecting paths is that the temporal ordering of the configurations might be used to speed up the roadmap connection phase, which generally accounts for most of the roadmap construction costs (typically more than 98%). In either case, the configurations generated can be free (i.e., collision-free configurations of the robot), or approximate (some penetration is allowed, which can be viewed as dilating the robot s free space [9]). Note that not necessarily all valid paths in a dilated free space can be transformed into valid paths in the original free space (since passages in the dilated space might not exist at all in the original space). Nevertheless, in many cases paths collected in the dilated free space can be pushed to the free space, and in addition, they may be easier for the operator to collect as they allow him more freedom of movement. We generate approximate configurations in two ways: original robot with penetration: the operator manipulates the original robot in the VE, but the system allows the robot to penetrate into the obstacles to some apriorifixed depth. reduced-scale robot with no penetration: the operator manipulates a reduced-scale robot which is not allowed to penetrate into the (original-sized) obstacles. The reduced-scale option is useful for certain types of robots since it may offer the operator an easier problem to solve (e.g., a golf ball fits more easily through a basketball hoop than does a basketball). In both cases, the planner interprets the configurations collected as configurations of the original-sized robot; it is its job to try to push any colliding configurations to the free space. 4.2 The Planner s Role The planner can help the operator by generating the easy portions of the path (by building a roadmap), and creating collision-free paths from approximate paths generated by the operator. If the operator has collected a free path, this can immediately be added to the roadmap. However, if an approximate path was collected, then the planner can incorporate only the free portions of this path and must try to push the colliding portions to the free space. One approach might be to use the colliding 4

6 configurations as milestones in the dilated freespace as in [9] or as seed nodes in OBPRM [3] (which attempts to push them to freespace). In this section, we describe more specialized methods for transforming colliding path segments to the free space. The motivation behind all these methods is that even though a node is in collision, there should be a free node nearby since the path was user-generated (using either haptic or visual interfaces) and so is expected to be close to a good configuration. Thus, the main challenge is determine the best direction in which to push the colliding segment. We have experimented with several different methods for performing this deformation which are described below. The general scenario we consider is as follows. We assume there is a single colliding portion of the path; if there is more than one, each one can be considered separately. We use c f and c l to denote the free nodes immediately preceding and following the colliding segment, and we let n c denote the number of configurations in the colliding segment. Generally, we we select n push = bc n c c of the colliding configurations to push to the free space, for some constant 0 <c1. (See Figure 2) Simple push In this method, we consider the straight line (in C-space) between c f and c l, and select k n push configurations evenly spaced on this line, for constant k 1. Each selected configuration on the collidingsegment is then paired with k of these intermediate configurations, and we try to push the colliding configurations in the direction of the intermediate configuration in search of a contact configuration. (See Figure 2(a)) Shortest push In this method, we attempt to find the shortest distance (in C-space) between a colliding configuration and the free space. In particular, we select a set of n push configurations evenly distributed on the colliding segment, and for each configuration selected, we perform a search to find the shortest distance that will transform that configuration to a free configuration. This is done by selecting d random directions (all perpendicular to the line connecting c f and c l ), and searching (in parallel) along those directions until finding the first free configuration. (See Figure 2(b)) Workspace assisted push In this method, we try to take more explicit advantage of the fact that the user-generated colliding path is usually quite close to a free path. In particular, we try to use geometric knowledge about the robot and the obstacles to select the direction in which to translate colliding configurations this direction is selected so as to move some colliding portion of the robot out of the obstacle. Again, we select some set of n push configurations evenly distributed on the colliding segment. For each configuration selected, we find the m closest pairs of vertices, one on the robot and one on an obstacle (we assume objects are modeled as polygons). For each vertex pair (v r ;v o ), we choose the direction from v r to v o,andtranslate the robot in that direction, looking for the first free configuration. (See Figure 2(c)). This type of translation can prove very useful if the robot is slightly penetrating an obstacle boundary. We note, however, that if rotation is required to transform the colliding configuration into a free configuration (e.g., if the robot has collision points on both sides of a narrow passage) then this method will fail. In current work, we are considering how to augment this method to detect when such movements are required. 5 Experimental Results In this section, we present the results of experiments designed to evaluate whether a human operator and an automatic motion planner can work together to solve a motion planning query. In particular, our experiments 5

7 (a) (b) (c) Figure 3: The workspace projection of the initial roadmap generated by OBPRM is shown in (a) with all obstacles present, and in (b) where some obstacles have been omitted to better show the roadmap. The improved roadmap which incorporated the operator generated approximate path is shown in (c). No Penetration Penetration Allowed Experimental Steps (original robot) (reduced-scale robot) new cfgs total cfgs cc new cfgs total cfgs cc create initial roadmap (OBPRM ) Approximate 1. add free cfgs Path 2. push to freespace none Critical Configs (only) Table 1: Statistics regarding roadmap improvement using operator supplied free paths (no penetration), approximate paths (penetration allowed), or critical configurations. The cc columns show the number of major components in the roadmap. were designed (i) to determine if haptic input is useful, and if so, to determine what kind of user-generated configurations (paths or critical configurations, and free or approximate) are most beneficial (Section 5.1), (ii) to evaluate our various pushing methods in terms of their ability to generate useful free configurations (Section 5.2), and (iii) to try to establish relationships between measurable quantities and the difficulty of a planning query for a human operator (Section 5.3). 5.1 Human/Planner Cooperation In these experiments, we investigated how a human operator and motion planner can cooperatively solve a motion planning query. The results reported below were obtained using a virtual environment consisting of 21 cubes of various sizes. An additional cube (the robot) was the only movable object in the scene. The obstacle cubes were arranged in such way that a path between opposite corners of the scene s bounding box must pass through several narrow corridors. (See Figure 3(a).) The experiments were structured as follows: 1. An initial roadmap is generated by OBPRM. 2. The human operator is shown this roadmap, and uses the PHANToM to generate configurations that might be helpful to the planner. 3. The initial roadmap was improved using the operator supplied configurations (and the simple push method if approximate paths were generated). The human operator was asked to collect: (i) free paths (no penetration allowed), (ii) approximate paths ( penetration allowed), or (iii) critical configurations. For the approximate path, instead of actually setting 6

8 a fixed amount of allowable penetration, we chose to scale the robot s size. This was easier to implement, and also offered the operator a smaller robot which is (visually) easier for him to maneuver in tight regions. We performed experiments using various scaling factors; the results reported here are for a scaling factors of 2=3 (small robot) and 1 (original size). The initial roadmap created by OBPRM had four big connected components and several small ones, each with less then three nodes (we stopped the planner at this point, since we did not want it to solve the problem on its own). Basically, the big connected components are located in the bottom-left, and the center and top-right regions of the environment (see Figures 3(a) and 3(b)). Table 1 lists some statistics regarding the roadmap improvement for free (no penetration) and approximate paths (penetration allowed), and critical configurations. In Summary, our conclusions are that the most useful configurations/methods for the planner are firstly, the critical configurations, secondly, pushing collidingpath segments to freespace, and finally, the free path segments directly collected by the user. Adding Paths. The operator s goal was to generate paths that could be used to connect the four major components of the roadmap into one large component. Collecting free paths using the original sized robot required rather delicate maneuvering in narrow corridors, which was rather difficult for the operator. Note that in this case, however, the planner could simply add the resulting path to the roadmap. The four major roadmap components were joined by adding 97 free path configurations. When paths were collected using the smaller robot, the operator had more freedom. However, this resulted in approximate paths, since more than half of the configurations corresponded to collision configurations for the original (unscaled) robot. We first added the (truly) free configurations, and then used the simple push method sketched in Section 4.2 to push the colliding segments into freespace. In this case, the number of roadmap components was first reduced to two by adding the free configurations, and then was further reduced to one after the colliding segments were pushed to the freespace. In both cases, the final connected component is distributed well over the environment, as can be seen in Figure 3(c) for the approximate path (reduced-scale robot) case. One observation we made was that, although it was possible to connect big connected components using our method for pushing paths to the surface, it might generate additional components since the nodes it generates are very close to C-obstacle surfaces in narrow passages. Adding Critical Configurations. In this case, the operator s goal was to select critical configurations which would be needed by the planner. One reason we were interested in this experiment is to see how much human help the planner needed to solve the query, i.e., did the planner really need the path, or would just the critical configurations suffice. In both cases (penetration allowed or not), it turned out that only ten critical configurations supplied by the operator were sufficient to enable the planner to connect the four major components into one large component. An additional benefit was that the resulting roadmaps were significantly smaller than in the approximate path case. One potential difficulty we observed was that since the operator selects critical configurations for the planner, he should have some knowledge of the planner s connection strategy. An alternative to this might be to let the local planner select critical configurations from an approximate path generated by the operator. 5.2 Evaluation of pushing methods In this section, we evaluate the various pushing methods described in Section 4.2 in terms of their ability to generate useful free configurations. In particular, we were concerned with their ability to generate so-called critical configurations of the robot that were inside narrow passages in C-space. In these experiments, the approximate paths (containing configurations with arbitrary penetration) were collected using a visual interface to the system. 7

9 (a) (b) (c) Figure 4: The flange problem is shown in (a) and (b): (a) a colliding configuration from the user-generated approximate path, and (b) the resulting collision-free configuration it was pushed to. For the alpha puzzle (c), we show a narrow passage configuration found by the workspace assisted push method. Flange Alpha Puzzle Push Method inside total success inside total success passage free rate passage free rate simple % % shortest % % workspace assist % % Table 2: Statistics regarding the various push methods. The results reported below were obtained using two environments: the flange and the alpha puzzle. The flange environment consists of a fixed rectangular part with a circular opening (the obstacle, 990 triangles) and a curved pipe (the robot, 5306 triangles) that must be inserted into the opening in the obstacle (see Figure 4(a).) The alpha puzzle environment consists of two identical twisted, intertwined tubes (one the obstacle and one the robot, 08 triangles each); the objective of the puzzle is to separate the tubes (see Figure 4(c).) (We worked with slightly easier versions of the models, which were obtained by scaling the pipe by a factor of.85 in the flange, and the obstacle tube by a factor of 1.2 in one dimension in the alpha puzzle.) For both environments, all three methods were tested on the same user-generated path. As our goal was to find configurations of the movable object (the robot) that lie in narrow passages in the C-space, we classified each of the free configurations generated from the collided configurations according to whether it was in the passage. A summary of the findings is contained in Table 2. The simple push method generated more configurations than by shortest push method because each configuration on the colliding segment was paired with several intermediate configurations (whereas the shortest push method generates only one configuration for each colliding configuration). Similarly, the workspace directed push method generates significantly more configurations than the others since many push directions (each corresponding to a pair of vertices (v r ;v o )on the robot and obstacle, respectively) were attempted for each colliding configuration. We note that the results from thesimple push and shortest push methods are consistentamong the two environments. In particular, both are fairly successful with about 90% of the generated nodes being inside the passage. Also, while simple push generates more passage nodes in total, shortest push generates a slightly higher percentage of passage nodes. We note that for both these methods to be most useful, the user-generated configurations must be close to the desired free configurations, and moreover, they must be sampled at a high enough frequency so that the resulting free configurations can be connected to complete the path. In terms of the workspace assisted method, the results at first appear somewhat disappointing 8

10 in relationship to the other methods. However, one must note that this method may try many unpromising directions since it selects vertex pairs based only only proximity information. We believe that the selection of the directions can be improved by considering the relative orientations of the surface normals of the object and robot. As opposed to the other two methods, we notice a slight difference in the performance of the workspace assisted method between the two environments. In particular, it does significantly better on the alpha puzzle than on the flange. This can be explained by the fact that the boundaries of the narrow passage in the flange are actually very thin, and so it is quite easy to push the configurations completely outside the passage. In contrast, the boundaries of the passage in the alpha puzzle are relatively thicker. Finally, we note that the workspace assisted method is generally slower than the others because it requires computing and sorting the distances between all vertex pairs. 5.3 Evaluating human planning difficulty In this section, we investigate whether any conclusions about the difficulty of a motion planning problem can be made using quantities measurable by the VE system. If so, they could be used, for example, to design a system that would automatically determine when the human operator needs more or less help, and then react accordingly (e.g., by reducing the size of the robot to make it easier to maneuver in crowded areas). The experiments were conducted using the 21 cube environment (See Figure 3). We collected statistics regarding quantities thought to relate to planning difficulty while the human operator was guiding the robot through the environment. The particular quantities we considered were the number of collisions, the robot s clearance (distance from the nearest obstacle), and the magnitude of the robot s reactive forces. The reactive force acting on the robot was measured every time the robot collided with an obstacle and is proportional to the depth of penetration. The factors varied in our experiments were operator skill, the size of the robot (a reduced-scale robot has more room to maneuver in narrow corridors, but may be harder to manipulate), and the robot s damping coefficient (a higher damping coefficient increases the robot s manipulability). Thus, each of these factors has its own contribution to the difficulty of planning. Unfortunately, they are not necessarily independent and it is hard to say which is dominant, particularly when one introduces the variable operator skill into the picture. To study these issues, we ran dozens of experiments using the same operators and environments. We observed that the operator had more control with a higher damping coefficient as that tended to reduce abrupt changes in the robot s velocity. The results, shown graphically in Figures 5 and 6 for a reduced-scale and original-sized robot, respectively, reinforce our intuition that a smaller robot is easier to maneuver. As can be seen in part (a), the path for the reduced-scale robot contains fewer collisions. Similarly, part (b) shows the clearance distance maintained between the robot and the nearest obstacle is larger for reduced-scale robot; note that both plots show similar patterns over time, but with the reduced-scale robot showing smaller fluctuations. This is because the clearance is an inherent characteristic of the obstacles, and therefore represents the (geometric) complexity of the environment. Similar observations can be made regarding the robot s reactive force (part (c)). As expected, the reduced-scale robot collides with obstacles less frequently than the original-sized one, and hence shows less frequent and often also smaller forces. In summary, we can say that the number of collisions, and the robot s reactive force, can be reduced by navigating with a reduced-scale robot. While we cannot say that the overall magnitude of the clearance can be reduced with a reduced-scale robot, it can reduce the frequency of fluctuations. Finally, while we had thought that the wall clock planning time would be shorter with a reduced-scale robot, this was not found to be true perhaps because all our operators were highly skilled, but also maybe because the running time is not a major factor deciding the difficulty of the environment. 9

11 6 Conclusions and Future Work This paper reports on our investigation regarding a hybrid (manual + automatic) motion planner which uses haptic and visual interfaces to enable a human operator and an automatic planner to cooperatively solve a motion planning query. Our results indicate that: Allowing the collection of approximate paths (either by allowing penetration, or by using a reducedscale robot) is easier for the operator, and, in certain situations, the use of a reduced-scale robot is easier for the operator to maneuver in crowded regions. The automatic planner can effectively transform approximate paths (containing collisions) into free paths. Roadmap visualization is useful. The operator s planning difficulty is correlated with easily measurable quantities such as the number of collisions, and the robot s clearance and reactive force. The above observations could be exploited in an adaptive system that would adaptively change the size of the robot in accordance with the current difficulty of the problem, e.g., reduce the size in hard regions and return to the original size in easier regions. This could be done automatically, in relation to the measured planning difficulty (e.g., collisions or contact force). Similarly, the planner could use these measures to identify difficult regions where it should concentrate. In general, the interface between the virtual and the physical world can filter/change the information returned to the human operator in such a way as to make it easier for the operator. References [1] J. M. Ahuactzin and K. Gupta. A motion planning based approach for inverse kinematics of redundant robots: The kinematic roadmap. In Proc. IEEE Int. Conf. Robot. Autom. (ICRA), pages , [2] N. M. Amato, O. B. Bayazit, L. K. Dale, C. V. Jones, and D. Vallejo. Choosing good distance metrics and local planners for probabilistic roadmap methods. In Proc. IEEE Int. Conf. Robot. Autom. (ICRA), pages , [3] N.M.Amato,O.B.Bayazit,L.K.Dale,C.V.Jones,andD.Vallejo. OBPRM:Anobstacle-basedPRMfor3D workspaces. In Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), pages , [4] J. Barraquand and J.-C. Latombe. Robot motion planning: A distributed representation approach. Int. J. Robot. Res., (6): , [5] N. Delson and H. West. Robot programming by human demonstration. In Proc. IEEE Int. Conf. Intel. Rob. Syst. (IROS), pages , [6] G. Z. Grudic and P. D. Lawrence. Human-to-robot skill transfer using the spore approximation. In Proc. IEEE Int. Conf. Robot. Autom. (ICRA), pages , [7] T. Horsch, F. Schwarz, and H. Tolle. Motion planning for many degrees of freedom random reflections at c-space obstacles. In Proc. IEEE Int. Conf. Robot. Autom. (ICRA), pages , [8] G.E.Hovlandandet al. Skill acquisition from human demonstration using a hidden markov model. In Proc. IEEE Int. Conf. Robot. Autom. (ICRA), pages , [9] D. Hsu, L. Kavraki, J-C. Latombe, R. Motwani, and S. Sorkin. On finding narrow passages with probabilistic roadmap planners. In Proc. Int. Workshop on Algorithmic Foundations of Robotics (WAFR), [] D. Hsu, J-C. Latombe, and R. Motwani. Path planning in expansive configuration spaces. In Proc. IEEE Int. Conf. Robot. Autom. (ICRA), pages , 1997.

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13 Number of Collisions Number of Collisions Time [Sec] (a) Accumulated collisions Time [Sec] (a) Accumulated collisions Clearance 12 8 Clearance Time [Sec] (b) Clearance Time [Sec] (b) Clearance Robot Force [N] Robot Force [N] Time [sec] (c) Contact force Time [sec] (c) Contact force. Figure 5: Reduced-Scale Robot: graphs depicting Figure 6: Original Sized Robot: graphs depicting time versus (a) total collisions, (b) robot s clearance (distance from nearest obstacle), and (c) con- 12 ance (distance from nearest obstacle), and (c) con- time versus (a) total collisions, (b) robot s cleartact force acting on the robot. tact force acting on the robot.