Local Path Planning with Proximity Sensing for Robot Arm Manipulators. 1. Introduction

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1 Local Path Planning with Proximity Sensing for Robot Arm Manipulators Ewar Cheung an Vlaimir Lumelsky Yale University, Center for Systems Science Department of Electrical Engineering New Haven, Connecticut 0650 Abstract In this paper, the problem of sensor-base path planning for robot arm manipulators operating among unknown obstacles of arbitrary shape is consiere. It has been known that, in principle, algorithms with proven convergence can be esigne for planar an simple three-imensional robot arms operating uner such conitions. However, implementation of such algorithms presents a variety of problems relate to covering the robot arm with a "sensitive skin", processing ata from large arrays of sensors, an esigning algorithms for step-by-step motion planning base on limite information. This paper escribes our first results of the implementation stuies on strategies for robot motion planning in an uncertain environment.. Introuction Ongoing research in robotic motion planning encompasses two major trens. In one approach, also calle the Piano Movers' problem, complete information about the robot an its environment is assume. A priori knowlege about the obstacles is represente by an algebraic escription such as a polygonal representation, an typically assumes an unchanging an static environment [7]. One avantage of the moel with complete information is in the possibility to observe an optimality criteria, such as minimum energy, or shortest path require to complete the task. An overview of the research in this area can be foun in []. Another approach to robot motion planning assumes incomplete information about the environment. Such a situation takes place, for example, when the robot has no a priori knowlege about the environment, but is equippe with a proximity sensor that notifies it of impening collision, or proximity to an obstacle. The area to be sense can be large such as with the use of ultrasonic range sensors [8] or stereo vision [9], or it can be a small local area if proximity sensors are use [4], such as the optical sensors iscusse in this paper. Other reporte uses of light in proximity sensors inclue grasping applications [0] where optical sensors are mounte in the robot gripper, an tactile sensors in fiber optic arrays []. It has been shown that the problem of moving a -egree of freeom two- or threeimensional manipulator in an environment with unknown obstacles can be reuce to the problem of moving a point automaton on the surface of a -imensional manifol where obstacles become simple close curves []. The algorithms resulting from this approach, calle Dynamic Path Planning (DPP), guarantee convergence, an require the arm to "slie" along or follow the contour of the obstacle. To realize such algorithms, the robot arm manipulator must have an ability to sense the presence of an obstacle by every point of its boy an to ientify the points of the boy that are in (physical or proximal) contact with the obstacle. To evelop this capability, a sensitive "skin" is neee that woul cover the whole boy of the arm. Such skin woul be similar, in case of the physical contact, to the skin of humans or animals; in case of the proximal contact, it woul form the kin of aura similar to the hairs on the legs of some insects. Realization of such sensing capabilities encompasses a variety of harware an ata processing issues that, to our knowlege, have not been aresse before. This paper aresses the implementation issues relate to the DPP approach, an, specifically, the problem of instrumenting a robot arm with the sensitive skin an interpreting the sensory ata generate by the skin, for the purposes of obstacle avoiance.

2 A scheme is suggeste for obstacle following given the response of the proximity sensors on the arm. The consiere approach is base on sensory ata supplie by infrare proximity sensors that cover the whole boy of the robot arm an thus forming the arm's "sensitive skin". The presente results escribe the first stage of our project an treat the problem in the context of motion planning for a planar robot arm. Suppose that the robot boy is covere by proximity sensors that sense a nearby obstacle. Assuming that a global path planning algorithm is in place, local strategy is neee to generate, at the current location of the robot, its next step. What is neee is the local tangent to the obstacle, at the point of contact with the robot; here, "contact" refers to the fact of sensing an obstacle at some istance. Once this is known, the robot can move along this local tangent to accomplish contour following. To generate the local tangent, information is neee on which points of the robot boy are experiencing the obstruction; this assures that the next move of the robot oes not lea to collision an/or loss of contact with the obstacle. Below, Section aresses the harware issues, escribes briefly available options, an justifies the choice of proximity sensors. Then, Section 3 aresses algorithmic issues of local step planning.. The Proximity Sensor Apart from proviing the robot arm with information about an approaching obstacle, the sensor system shoul also inicate the location on the arm boy where the obstruction takes place. This suggests an array of istance sensors. A useful etection range of about five inches is consiere to be aequate. The sensor shoul remain effective uner shallow angles between the obstacle an the sensing beam, an shoul furthermore have no "ea zones" on the arm boy: an obstacle must be etecte if it is locate within the etectable range of the sensors. Otherwise, if the ea zone comes in contact with an obstacle, a collision may take place. A brief survey of sensor options follows. The first choice to be mae is between passive sensors, such as tactile or vision, an active sensors that operate on emitting a form of energy an sensing the reflecte signal. For the consiere application, passive sensors o not seem to present a viable alternative. For example, tactile sensing of obstacles in practice woul amount to numerous collisions, whereas covering the arm boy with sensors, each of which woul provie a vision capability, is not practical. Thus, a viable choice must be among active sensors. Two major types of active sensing make use of optical or acoustical raiation. In aition, inuctive an capacitive methos can be use to accomplish sensing, but these methos are generally limite to etection istances of less than one inch, an are epenent on the material of the obstacle. Commercial inuctive an capacitive sensors are mainly use in inustrial environments where the applications require urability an involve objects of known composition that have to be sense at very close range. With acoustic sensing, a burst of ultrasonic energy is transmitte, reflecte from an obstacle an then receive, making use of the time of flight for istance measurement [5]. A rawback of this type of sensor is that, because the wavelength of soun is relatively long, some obstacles can exhibit specular (mirror like) reflection. Consequently, large flat surfaces may be unetecte by the sensor because of the lack of reflecte signal. This effect is especially pronounce at shallow angles between the energy beam an the obstacle - a case very common in the consiere application. In aition, commonly available acoustical sensors, such as the popular Polaroi sensor, operate poorly when obstacles are place closer than 0.9 feet from the sensor [5,8], unless methos such as active amping of the transucer are use [6]. This ea zone necessitates the path planner to restrict the istances of obstacle etection to larger than 0.9 feet from the sensor, which is not realistic in the case of motion planning for arm

3 3 manipulators. For example, it may rener the target position unreachable if it can be reache only by passing between two obstacles locate at about two feet from each other. To overcome some of these shortcomings, a raiation of shorter wavelength can be use, such as light. The wavelength of visible light is in the range of hunres of nanometers, tening obstacles to appear matte, scattering light equally in all irections [3]. If the matte surface to be sense is illuminate by a narrow beam of light, the amount of reflecte raiation will epen mainly on the istance between the surface an the receiver. This insensitivity to obstacle orientation can be exploite to etect the presence of objects. One rawback of using light for sensing is that objects of ark colour may not be sense; also, optical mirrors will continue to exhibit specular reflection, possibly resulting in a lack of returning raiation. Base on these consierations, a sensor system was chosen base on infrare proximity sensors. The transmitte light is infrare (IR), at a wavelength of approximately 875 nm. This light is moulate at a frequency of 0 khz, an is then coherently etecte after reception to improve immunity to other light sources, such as room lighting. The reflecte light is emoulate by a phase locke loop, amplifie, an then passe to a igitizer. In the current esign, sixteen sensor pairs each consisting of a transmitter an receiver are time multiplexe together, forming one sensor moule. The moule is manufacture so that all optical components an instrumentation are on one printe circuit boar. A sketch of the moule appears in Figure, an a photograph of a part of the actual moule is given in Figure 3; note two sensor pairs highlighte by the reflection in the mile of the black acrylic. The entire sensor system is comprise of a number of these sensor moules mounte on the arm, Figure 4. In the evelope sensor system, the amplitue of the reflecte light is use for proximity measurement. An alternative approach, often use in auto focus cameras, is to emit a beam of light an use triangulation to etermine istance. The avantage gaine by the triangulation metho is that the object colour has a reuce effect on the measure istance; on the other han, optical mirrors continue to be ifficult to etect. sensor pair printe circuit boar black acrylic Figure. A sketch of the sensor moule. A typical sensor response is shown in Figure. The sensor sensitivity becomes insufficient beyon a istance of five inches. If neee, sensing beyon this istance coul be supplemente by an acoustical sensor; increasing the transmitte power presents another option.

4 4 0 8 Output (V) istance,inches Output (V) Figure. A typical response of the infra-re sensor. 3. Step Planning an Contour Following In aition to the information about contact with an obstacle provie by the proximity sensor escribe above, information on the location of the obstacle relative to the arm is also available. It will be shown now how this ata is use for contour following. Since the contour following algorithm works in conjunction with the global path planning algorithm [], the latter is first briefly iscusse below. T S Figure 5. Configuration space of robot arm. Assume that the robot arm presents a two-link planar structure with two revolute joints an, Figure 7. The robot task is to procee, collision-free, from point S (Start) to point T (Target). Assume for the moment that the robot boy is covere with tactile sensors. [Actually, the algorithm can work with any type of proximity sensing]. The robot can be represente by a point automaton in the configuration space (, ), Figure 5. Corresponingly, any obstacle in the work space has its image in the configuration space. In the path planning algorithm, the automaton moves irectly to T from its start S along the line segment S - T until an obstacle is encountere. The point of contact is then esignate as a hit point. The automaton turns in a prespecifie local irection (e.g. left, as in Figure 5) an follows the contour of the obstacle until the line segment S - T is again met at istance from T shorter than the lastly efine hit point. At this point, the automaton follows S - T to T, unless another obstacle is met causing the process to repeat. The algorithm has been shown to converge if the target is reachable, or to conclue in finite time that the target is not reachable if this is the case.

5 5 local tangent obstacle automaton Figure 6. Using the local tangent for contour following. To realize contour following require by the path planning algorithm, a proceure is neee to plan the next little step along the obstacle bounary at a given location of the robot arm. The input information for the proceure is the current location of the arm an the local tangent to the obstacle bounary, Figure 6. The calculation of the local tangent requires the information on what point(s) of the robot boy are in contact with the obstacle in the work space. Note that contour (obstacle) following requires no information about the shape of the obstacle in work space or in configuration space. Below, the proceure for calculating the local tangent is escribe, followe by the algorithm that uses the local tangent for planning the next step along the obstacle bounary. Calculation of Local Tangent The following erivations are vali for a egrees of freeom (of) revolute - revolute (articulate) arm, Figure 7, but can be similarly erive for other kinematic configurations. y L obstacle P ß M 3 ß 4 C l l J B l x Figure 7. A sketch of the -link arm with revolute joints. O J In Figure 7, link an link of the arm are represente by the line segments O - B an B - P, of lengths l an l, respectively; J an J are arm joints; point P represents the arm wrist; point B, which coincies with joint J, represents the arm elbow. Whenever an obstacle is encountere, the arm attempts to slie along its surface. This sliing is accomplishe by a coorinate move between joints J an J, base on the value of the local tangent LM. To fin the latter, estimates of the erivatives an are compute at every point along the contour, using the proceure escribe next.

6 6 Depening on their location relative to the arm, obstacles that may occur in the work space are ivie into three categories, easily recognizable by the sensor system: type I, type II, an type III, Figure 8. Now we consier each of the types. III arm II I Figure 8. Obstacle types. Type I are those obstacles that obstruct link. It is obvious that since link is irrelevant in such cases, then = 0 an 0. Therefore, the local tangent in this case is vertical. Type II are those obstacles that obstruct link. Assume that the arm is obstructe at point C by a type II obstacle, locate at link at the istance l from the the joint J, Figure 7. Then, the estimates of an at C can be foun as follows. Write the expressions for the x an y coorinates of C, c x an c y respectively: c x = l cos( ) + l cos ( + ) () c y = l sin( ) + l sin ( + ) Take total erivatives: c x =-l l sin( ) +l cos( + )-l sin( + ) -l sin( + ) c y =l l cos( ) +l sin( + )+l cos( + ) +l cos( + ) Since C is a stationary point, c x =c y =0. Fin l from both equations of (): an l = [-l cos -l cos( + )] -l cos( + ) sin( + ) 3 l = [l sin +l sin( + )] +l sin( + ) cos( + ) 4 Equating the right han sies an eliminating the enominators in (3) an (4), obtain: cos( + ) -l cos -l cos( + ) -sin( + ) l sin +l sin( + ) =l cos ( + )+sin ( + ) 5 Now, the ratio / is foun as = l -l cos cos + -l sin sin + -l = - l l cos cos + + sin sin After simplification, the local tangent to a type II obstacle at point C is given by:

7 7 = - l l cos + 7 Type III are those obstacles that obstruct the arm wrist or elbow (points P an B, Figure 7). To fin the local tangent in this case, the inverse Jacobian of the arm is use []. Denote x = P x an y = P y in case the wrist is obstructe, an x = B x an y = B y in case the elbow is obstructe. Then, the following relationship hols: = l cos + x + l sin + y l l cos = -l cos -l cos + x - l cos -l cos + y l l cos 8 It is esire that the wrist P slies along the obstacle, which correspons to moving along the line segment LM, Figure 7. Define ß 3 as the angle between the line perpenicular to link an the line from P to the obstacle, an ß 4 as the angle between the line LM an the positive x-axis. Then, y x = tanß 4 / : or y = x tanß 4 9 where ß 4 = + + ß 3. Substituting the expression for y from (9) into (8), obtain the ratio = - l cos +l cos cos -l sin sin + l sin + l sin cos +cos sin tanß 4 l cos cos -sin sin + sin cos +cos sin tanß 4 After simplifying, the expression for the local tangent in the case of a type III obstacle appears as: = - l l + cos + sin tan + ß 3 cos + sin tan + ß 3 (0) Step Planning Algorithm Every point of contact between the arm boy an an obstacle has an associate sensor pair that oes the corresponing obstacle etection. For every sensor pair that etects an obstacle, a local tangent is calculate base on the metho escribe above. The motion of the point automaton along a local tangent in configuration space correspons to the arm "sliing" along the obstacle at the point of contact in the work space. This process is repeately one uring contour following. Note that one or more obstacles can be sense simultaneously by more than one sensor pair. If the chosen local irection is "left", Figure 6, meaning that the robot arm shoul maneuver aroun the obstacle in a clockwise fashion, a counterclockwise (ccw) rotation of the calculate local tangent will cause the robot arm to move away from the obstacle, Figure 9. Thus, if the arm is too close to the obstacle, the local tangent can be rotate ccw slightly to increase the istance to the obstacle. The reverse can be one if the sense obstacle is still at a large istance from the arm. No ajustment is mae to the tangent to be followe if the istance to the obstacle is at some preset nominal value. This feeback in the sensor-

8 8 base control loop results in constant istance tracking between the arm an the obstacle, thus improving contour following. tangent rotate ccw local tangent Figure 9. Configuration Space: rotation of local tangent (ccw) causes the robot to move away from the obstacle. If more than one sensor pair senses one or more obstacles simultaneously, more than one local tangent will be calculate. Then, one of these tangents is selecte for planning the next step. The following two examples illustrate this point. B P O (a) (b) E Figure 0. a) Work space, b) configuration space. Example. Suppose the robot arm is moving towars point P, in the irection of increasing, Figure 0b. At this point the arm is obstructe by obstacle, which presents an obstacle of type II, Figure 0a. The local tangent at P is EB. In the vicinity of point P, a further increase in will cause collision with the obstacle, Figure 0a. If the local irection is "left", the next move along EB towars point B will cause the arm to slie along obstacle to the position inicate by the otte line in Figure 0a. Continual recalculation an motion along the resultant tangent constitutes the process of contour following. B C A P 3 O F E (a) (b) D Figure. a) Work space, b) configuration space. Example. For the case with multiple obstructions, suppose the robot arm is moving in the irection of increasing, Figure b. At point P, the arm is now obstructe by three obstacles that are sense by the sensor system, Figure. A local tangent is then calculate for each obstacle. Obstacles,, an 3, of type I,II, an III, prouce tangents CD, BE, an AF respectively. For the local irection "left", the robot can move towars one of the points A,B or C. It is clear from Figure that moving in the irection of point C will cause collision with obstacles an 3. Similarly, moving towars point B will cause collision with obstacle 3. Moving towars point A will cause no collision, an is

9 9 therefore the chosen move. The arm moves away from obstacles an, an follows obstacle 3's contour. Analogously, a local irection "right" woul necessitate a move towars point F for correct contour following. The system escribe above has been implemente on a PUMA 560 robot arm, using only the secon an thir egrees of freeom of this arm. In the present configuration, the real time control system is base on two istribute control boars from Pacific Microcomputers, each of which inclues one Motorola 6800 microprocessors, Mbyte of RAM, an Input / Output (I/O) ports. The first boar hanles the sensor I/O, processing of raw sensor ata, an the calculation of local tangent when obstacles are encountere. The secon boar hanles the path planning tasks an I/O functions for the robot servo controls. Combine with the DPP global path planning proceure, the two algorithms escribe above for step planning an local tangent calculation, prove effective in accomplishing the path planning tasks. In the experiments with various combinations of obstacles, no contact has ever been mae with the obstacles, so no collision occurre. No a priori information about the obstacles were given to the robot; path planning was accomplishe base only on the on-line information from the sensor system. As anticipate, the require ata processing was not significant an fit rather easily into the real-time operation. One of the experimental set-ups, with a C-shape obstacle, is shown in Figure 4. References. C.K. Yap, Algorithmic Motion Planning. Avances in Robotics, vol. : Algorithmic an Geometric Aspects, (J.T. Schwartz an C. Yap, Es.), Hillsale, New Jersey: Erlbaum, V. Lumelsky, Dynamic Path Planning for a Planar Articulate Robot Arm Moving Amist Unknown Obstacles, Automatica, Sept D. Ballar, C. Brown, Computer Vision, Prentice-Hall, New Jersey, M.Winston, Opto Wiskers for a Mobile Robot, Robotics Age, Vol. 3 #, New Jersey, Ultrasonic Range Finers, Polaroi Corporation, G.L.Miller, R.A.Boie, an M.J.Sibilia, Active Damping of Ultrasonic Transucers for Robotic Applications, Proc. IEEE International Conference on Robotics, Atlanta, Georgia, March J.T. Schwartz an M.Sharir, On the Piano Movers' Problem: I. The Special Case of a Rigi Polygonal Boy Moving Amist Polygonal Barriers, Comm. Pure Appl. Math. 4, A. Elfes, Sonar-Base Real-Worl Mapping an Navigation. IEEE Journal of Robotics an Automation, June L. Matthies an S.A. Shafer, Error Moeling in Stereo Navigation, IEEE Journal of Robotics an Automation, June D.J. Balek an R.B. Kelly, Using Gripper Mounte Infrare Proximity Sensors for Robot Feeback Control, Proc. 985 IEEE Conference on Robotics an Automation, St.Louis, Missouri, March J.S. Schoenwal, A.W. Thiele an D.E. Gjellum, A Novel Fiber Optic Tactile Array Sensor, Proc. 987 IEEE Conference on Robotics an Robotics an Automation, Raleigh, North Carolina, April R.P. Paul, Robot Manipulators: Mathematics, Programming, an Control, MIT Press, 983.

10 0 Figure 3. Sensor moule. Figure 4. An experimental set-up with a C-shape obstacle.

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