On the meaning of computer models of robotenvironment

Transcription

1 University of Woongong Research Onine Facuty of Informatics - Papers (Archive) Facuty of Engineering and Information Sciences 007 On the meaning of computer modes of robotenvironment interaction Urich Nehmzow University of Essex Phiip J. McKerrow University of Woongong, phiip@uow.edu.au Steve Biings University of Sheffied Pubication Detais Nehmzow, U., McKerrow, P. J. & Biings, S. 007, ''On the meaning of computer modes of robot-environment interaction'', Proceedings TAROS'07: Towards Robots and Systems, University of Waes, Aberystwyth, pp Research Onine is the open access institutiona repository for the University of Woongong. For further information contact the UOW Library: research-pubs@uow.edu.au

2 On the meaning of computer modes of robot-environment interaction Abstract The meaning of a computer mode a computer simuation of some physica system is an i-defined concept, and ceary it woud strengthen any hypotheses based on such modes if some forma mode verification was possibe. In this paper we present experiments on computer modeing of mobie robot operation, in which the interaction of a Scitos G5 mobie robot with a carefuy chosen environment is modeed. The experimenta setup chosen was such that we coud determine from theoretica considerations what the mode shoud be. The comparison between the actuay obtained computer mode and the theoreticay correct soution demonstrates that in the experiments conducted the obtained modes are correct. Discipines Physica Sciences and Mathematics Pubication Detais Nehmzow, U., McKerrow, P. J. & Biings, S. 007, ''On the meaning of computer modes of robotenvironment interaction'', Proceedings TAROS'07: Towards Robots and Systems, University of Waes, Aberystwyth, pp This conference paper is avaiabe at Research Onine:

3 On the Meaning of Computer Modes of Robot-Environment Interaction Urich Nehmzow 1, Phiip McKerrow and Steve Biings 3 1 University of Essex, UK University of Woongong, Austraia 3 University of Sheffied, UK Abstract The meaning of a computer mode a computer simuation of some physica system is an i-defined concept, and ceary it woud strengthen any hypotheses based on such modes if some forma mode verification was possibe. In this paper we present experiments on computer modeing of mobie robot operation, in which the interaction of a Scitos G5 mobie robot with a carefuy chosen environment is modeed. The experimenta setup chosen was such that we coud determine from theoretica considerations what the mode shoud be. The comparison between the actuay obtained computer mode and the theoreticay correct soution demonstrates that in the experiments conducted the obtained modes are correct. 1. Correctness of Numerica Modes of Physica Systems 1.1 Mode Verification (Oreskes et a., 1994) have convincingy argued that a forma verification and vaidation of numerica modes of natura systems is impossibe. By verification they mean a demonstration of truth, forming a reiabe basis for decision making. Such verification, they argue, is ony possibe for cosed systems, and since a interesting systems, such as physica systems ike robots are open, a forma demonstration of truth is impossibe. There is the further diemma that often more than one mode wi produce the same output (non-uniqueness of modes). This impies that a mode generating the correct output need not be the right one a probem we are interested in with regard to this paper. 1. Mode Vaidation (Oreskes et a., 1994) argue further that even the weaker notion of mode vaidation, which they define as the estabishment of egitimacy (modes not containing interna faws), may not be a usefu concept for physica systems. They argue that even if a mode produces the correct numerica output this does not prove that the mode is actuay an accurate representation of the rea system. We beieve that mobie robotics is an idea experimenta medium to investigate the question of mode verification and vaidation. Because the experimenta scenario can be tighty controed by the experimenter, it is possibe to design experiments in which the correct mode is known before the modeing process. This is what we have done in the experiments presented in this paper. We designed three experiments with a Scitos G5 mobie robot, in which it was possibe to formuate the reationship between mode input and mode output in cosed mathematica form; in other words, the correct mode was known to us a priori, because of the experimenta setup chosen. We then obtained a numerica mode of the input-output reationship, using a system identification approach, and evauated the resuting mode in the ight of our theoretica knowedge. 1.3 Background: Numerica Modeing of Robot-Environment Interaction We have shown previousy that it is possibe to express certain input-output reationships pertaining to a (mobie) robot s interaction with its environment in cosed mathematica form (Nehmzow, 006). For instance, it is possibe to express sensor-motor coupings (i.e. robot contro code) in the form of non-inear poynomias (Igesias et a., 004, Igesias et a., 007). Simiary, it is possibe to express sensory perception as a function of robot ocation (Nehmzow, 006, p.156ff) simuation of sensory perception or its counterpart, the robot s ocation as a function of sensory perception (Nehmzow, 006, p.16ff), i.e. sef-ocaisation. Such representations are extremey usefu for the robotics practitioner to express reevant reationships succincty and parsimoniousy, to program robots in very efficient ways, or to anayse the robot s behaviour formay. It is the atter point that this paper is con-

4 cerned with. A mode such as the one shown in equation 1, which gives a wa-foowing robot s x(t) position as a function of aser perception L, begs the question whether this mode is the true reationship between perception and ocation, or merey one of many possibe representations of that reationship. In other words: what is the meaning of such a mode? x(t) = 1.04x(t 1) 0.65y(t 1) (1) 6.7L 15 (t) 8.84L 30 (t) L75 (t) +7.1L 10 (t) 5.75L 135 (t) L 180 (t) If the modeing process is to enabe understanding of mobie robot behaviours, if it is to hep us grasp the connection between perception and action, then we need to be abe to assign meaning to the poynomia. That is, the coefficients of the poynomia are not just numbers in a regression equation, but vaues that represent rea reationships in the physica word of mobie robot contro. The answer to this question heps us to answer a deeper question: Can we capture the behaviour of a robot in an equation that we can understand and therefore use to vaidate that a design is working correcty? Deeper sti, Can we use this understanding to deveop toos for the design of robot behaviours? If we can do the first, we can verify that a robot is achieving its design goas. This woud be a big step forward in mobie robot design. The second question is beyond the scope of this paper, but naturay foows on from this research. 1.4 Modeing mobie robot behaviours Mobie robots perform tasks that invove motion. Motion may be veocity controed or position controed. They perform those tasks within an environment and, so, their behaviour is infuenced and effected by that environment. Thus, when achieving a given task, a robot s behaviour is considered to emerge from the interaction of the robot with the word. The reationship between the task, the robot and the environment is a robot behaviour that describes the interaction between the robot and the environment as it achieves the task. Usuay, more compex environments require more compex behaviours. The hypothesis that underies this research is that that interaction can be modeed by a function that can be found by observing the robot s behaviour. A user requests a robot to carry out a task (figure 1). From this request, a trajectory, a pan or a goa is produced that sets the robot in motion. As the robot moves, it interacts with the word and that interaction resuts in changes to the robot s motion. After a sequence of motions and interactions the robot competes its task. By Task Robot Word Figure 1: Reationship between Task, robot and environment moving, the robot has changed the state of the word, which in some way wi modify the next task. The arrows in figure 1 indicate the direction of causaity. The task causes the robot to move, not vice versa. The commands to the robot resut in its motion, which can be considered to be a forward process that is a oneto-one mapping. The inverse process of trying to infer the commands from the motion is potentiay a one-tomany process and is much harder to mode. The robot, by achieving the task, changes the state of the word. Again this is a forward process with a one-to-one mapping. Trying to infer the task from the change in the state of the word is an inverse process that may have a one-to-many mapping. Simiary, inferring a robot s ocation from its sensor data is a many-to-many mapping that we try to fuse into a many-to-one mapping in ocaisation. 1.5 Mobie robot action behaviours A mobie robot is a machine that moves in (x, y, θ) coordinates. Its motion can be decomposed into severa basic behaviours: 1. Transation by a distance d in a straight ine from point (x 1, y 1 ) to (x, y ).. Rotation by an ange θ from heading θ 1 to θ. 3. Combined transation and rotation from point to point aong a curved path. 4. Linear veocity v r in the heading θ. 5. Rotationa veocity ω r around the point (x, y). 6. Combined inear and anguar veocity to foow a trajectory from (x 1, y 1, θ 1 ) to (x, y, θ ). Any motion of a mobie robot can be described by a combination of these action behaviours. Higher-eve behaviours combine these action behaviours with perception behaviours to enabe a mobie robot to interact with the word to perform a task. To vaidate the hypothesis that we can capture the behaviour of a robot in a NARMAX mode that we can understand, we designed a set of experiments. The aim of each experiment is to produce a situation where we know what the poynomia shoud be a priori, and then examine the NARMAX mode to see how we it matches the expected poynomia.

5 The design of the foowing experiments was guided by the aim of producing a simpe task where we: 1. know the poynomia a priori,. use one action behaviour, 3. test either the action behaviour or contro an action behaviour to achieve a perception behaviour, and 4. we modify one of the three components in the TaskRobot-Word reationship in a known way and mode the reationship between the other two. In this way, it shoud be possibe to reduce the system to its underying components. 1.6 Experimenta Setup In order to investigate the question posed in section 1.3, we investigated three scenarios of robot-environment interaction, in which the mathematica reationship between the variabes under consideration was known a priori, to see if the mode resuting from our modeing process took the form that we knew to be correct. Specificay, we investigated the foowing three scenarios: 1. A mobie robot moves in a straight ine aong a sinusoida wa, and we mode the range reading of the wa-facing sensor as a function of position. The action behaviour is transation at a fixed veocity. The perception behaviour is to measure the shape of the wa.. A mobie robot foows a straight wa in a sinusoida fashion, and again we mode the range reading of the wa-facing sensor as a function of position. The action behaviour is combined transation and rotation from point to point aong a curved path. The perception behaviour is to cacuate the pose of the robot (position and bearing) reative to the straight wa and then measure the distance from the robot to the wa with the aser range finder. 3. A mobie robot is paced at an unknown position in a circuar environment, and we mode the robot s position (x, y) as a function of the robot s sensory perception. The action behaviour is to stand sti. The perception behaviour is to measure the ranges to the was in front and behind the robot. (a) (b) Figure : (a) Dax. The robot s aser range finder has an anguar coverage of 40, with a radia resoution of 0.36 and distance resoution of ess than 1 cm. To decrease the dimensionaity of the input space to the Narmax mode, we coarse coded the aser readings into 10 sectors (u1 to u10 ) by averaging 6 readings for each 4 degree intervas (b).the robot s two degrees of freedom used here were transationa and rotationa veocity. Positive and negative transationa veocities indicate forward and backward movement respectivey. Positive and negative rotationa veocities indicate eft and right turns respectivey. The robot used was the Scitos G5 mobie robot Dax (figure ), equipped with a ring of 4 sonar and 4 infrared sensors, both uniformy distributed. A Hokuyo aser range finder is aso present on the front part of the robot. This range sensor has a wide anguar range of 40 with a radia resoution of 0.36, and distance resoution of ess than 1 cm. The robot s coour camera (640x480 pixes at 60 Hz) was not used in the experiments reported here. Modes of the form given in equation 1 were obtained using the Narmax system identification process (Biings and Chen, 1998), (Korenberg et a., 1988, Biings and Voon, 1986), which is a parameter estimation methodoogy for identifying both the important mode terms and the parameters of unknown noninear dynamic systems. For mutipe input, singe output noiseess systems this mode takes the form of equation. y(n) = f (u1 (n), u1 (n 1), u1 (n ),, u1 (n Nu ), () u1 (n), u1 (n 1), u1 (n ),, u1 (n Nu ),, u1 (n), u1 (n 1), u1 (n ),, u1 (n Nu ), u (n), u (n 1), u (n ),, u (n Nu ), u (n), u (n 1), u (n ),, u (n Nu ),, A experiments described in this paper were conducted in the 100 square meter circuar robotics arena of the University of Essex. The arena is equipped with a Vicon motion tracking system which can determine the robot s position in 3D at a samping rate of 100 Hz with sub-miimetre accuracy. u (n), u (n 1), u (n ),, u (n Nu ),, ud (n), ud (n 1), ud (n ),, ud (n Nu ), ud (n), ud (n 1), ud (n ),, ud (n Nu ),, ud (n), ud (n 1), ud (n ),, ud (n Nu ),

6 Figure 3: Experimenta setup for the first experiment: the robot drives in a straight ine aong a sinusoida wa Figure 4: Range data ogged in the first experiment y(n 1), y(n ),, y(n N y), y(n 1), y(n ),, y(n N y),, y(n 1), y(n ),, y(n N y) ) y(n) and u(n) are the samped output and input signas at time n respectivey, N y and N u are the regression orders of the output and input respectivey, d is the dimension of the input vector and is the degree of the poynomia. f() is a non-inear function and here taken to be a poynomia muti-resoution expansion of its arguments. Expansions such as muti-resoution waveets or Bernstein coefficients can be used as an aternative to the poynomia expansions considered in this study.. Robot Experiments.1 Experiment 1: Foowing a sinusoida wa In the first experiment we drove Dax in a straight ine aong a sinusoida wa, this experimenta scenario is shown in figure 3. We coected range data from the robot s wa-facing aser range sensor during 13 traversas of the route, this ogged data is shown in figure 4. We removed the DC component (mean) from the ogged data and subsamped it so that 10 samping points per period remained, and modeed it using an Armax process (Inria, 007). Knowing that the wa is as much as experimentay possibe sinusoida, we expect to obtain a mode of the form d(t) sin(t). The mode we actuay obtained is given in equation 3, and appears to have a different form at first sight. d(t) = 0.9 d(t 1) d(t ) 0.7 d(t 3) (3) Origina output Mode predicted Data point Figure 5: Actuay observed sensor reading and time series generated by equation 3. However, under the assumption that d(t) = sin(t) and for a sufficienty high samping rate (i.e. sma t) equation 3 can be rewritten as shown in equation 4. d(t) =.9 d(t 1) +.14 d(t ).7 d(t 3) (4) =.9 sin(t t) +.14 sin(t t).7 sin(t 3 t) =.9 (sin tcos t cos tsin t) +.14 (sin tcos t cos tsin t).7(sin tcos 3 t cos tsin 3 t).9 sin t +.14 sin t.7 sin t = 0.34 sin t. Equation 4 therefore confirms our expectation that the mode obtained refects the true reationship between the modeed variabes. However, it aso iustrates that the output from the modeing process may not resembe the

7 a priori mode. In such cases, as in this exampe, it is unwise to immediatey jump to the concusion that the mode isn t correct. We may, as here, need to reformuate the equations in the mode.. Experiment : Sinusoiday foowing a straight wa The second experiment is essentiay a variant of experiment 1, this time however the environment is simpe whie the robot s behaviour is more compex : the robot foowed a straight wa, whist its steering commands were governed by the mathematica sine function. This experimenta setup is shown in figure Origina output Mode predicted Data point Figure 8: Actua range data, and mode-predicted range data As before, we modeed the perceived distance d as a function of t, expecting a reationship d(t) sin(t). The actua mode obtained is given in equation 5. d(t) = 1.6 d(t 1) d(t ). (5) Rewritten as previousy discussed (equation 4) this becomes d(t) 0.6 sin t, again confirming our expectation. Figure 6: Experimenta setup for the second experiment: the robot drives in a sinusoida ine aong a straight wa We ogged the range reading of the robot s aser range sensors during 9 passes aong the straight wa, the robot s perceived distance to the wa is shown in figure 7..3 Experiment 3: Sef-ocaisation in a circuar arena In our fina experiment we paced Dax in a circuar arena (as much as this was experimentay possibe), as shown in figure 9. Figure 7: The robot s perceived distance to the wa in the second experiment Figure 9: Experiment 3: Perception-based ocaisation in a circuar arena Here, we were interested in modeing x and y (defined

8 in figure 10) as a function of the robot s aser range readings. The theoretica soution, derived from figure 10, is given in equation 6. y D f D b (X,Y ) c c (X,Y ) r r (X c, Y c ) Figure 10: Experiment 3: Definitions 1= robot position 0 01 y c = D f + D b y r + D f = y c y r D b = y c D b y r = y c y r + D f = D b y r y r = D b D f y r = 0.5 D b 0.5 D f, (6) with D f and D b being the range readings at the front and back of the robot respectivey. Anaogousy foows x r = 0.5 D eft 0.5 D right. (7) Having ogged a aser range readings L over the entire arc of 40 avaiabe from the Hokuyo aser range finder, the Narmax modeing process determined the mode of the robot s (x r, y r ) position as a function of L given in equation 8. This mode is very cose to the ground truth estabished by the theoretica considerations of equations 6 and 7. x r = 0.0m 0.50 D D 183 (8) y r = 0.0m 0.51 D D Discussion Computer modeing of robot-environment interaction is an important simuation too for the roboticist, but we woud argue that understanding, identifying the underying dynamics of that interaction are an equa, if not more x important contribution of computer modes towards a science of mobie robotics. A key issue in computer modeing of mobie robot operation is, obviousy, the veracity of the computer mode it is conceivabe that a computer mode merey captures the input-output reationships of the modeed system, or that it actuay represents the true reationship between these variabes, both staticay and dynamicay. Many modeing methods, for exampe artificia neura networks, capture the former, but are in no way a true representation of a physica systems s input-output dynamics. In contrast to such opaque modeing methods, the Narmax method used here is capabe of identifying true input-output reationships (Zhu et a., 006, Swain et a., 1998), and is therefore particuary interesting for a forma anaysis of robot-environment interaction. Most modeing methods are we abe to aow predictions of system states, but fai to mode the system s underying dynamics. Narmax methods have been shown to capture the dynamics of physica systems (quaitative vaidation, (Zheng and Biings, 1999, Haynes and Biings, 1994)), and ongoing work in our aboratories investigates this property with respect to mobie robot dynamics. Our experiments with a Scitos G5 robot, reported in this paper, indicate that it may we be the case that we can capture the true reationship between input and output variabes, rather than just generating an agreement between their numerica vaues. We designed three experiments in which the correct mode was know to us a priori, and found that in a three cases the Narmax system identification process indeed obtained the correct mode. Acknowedgements The research presented in this paper was supported by the British Engineering and Physica Sciences Research Counci under grant GR/S30955/01, we acknowedge this support gratefuy. We aso thank Christoph Weinrich of the Technica University Imenau, who carried out the experimenta work reported in this paper. References Biings, S. and Chen, S. (1998). The determination of mutivariabe noninear modes for dynamica systems. In Leonides, C., (Ed.), Neura Network Systems, Techniques and Appications, pages Academic press. Biings, S. and Voon, W. S. F. (1986). Correation based mode vaidity tests for non-inear modes. Internationa Journa of Contro, 44: Haynes, B. and Biings, S. (1994). Goba anaysis and quaitative mode vaidation in noninear system identification. Noninear Dynamics, 5: Igesias, R., Kyriacou, T., Nehmzow, U., and Biings, S. (004). Task identification and characterisation in mo-

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