To be presented at the IEEE Intelligent Robot Systems Conference (IROS), Victoria, B.C., Canada, October 1998AbstractHydraulic machines used in a number of applications arehighly non-linear systems. Besides the dynamic couplingbetween the different links, there are significant actuator non-linearities due to the inherent properties of the hydraulic sys-tem. Automation of such machines requires the robotic machineto be atleast as productive as a manually operated machine,which in turn make the case for performing tasks optimallywith respect to an objective function (say) composed of a com-bination of time and fuel usage. Optimal path computationrequires fast machine models in order to be practically usable.This work examines the use of memory-based learning inconstructing the model of a 25-ton hydraulic excavator. Thelearned actuator model is used in conjunction with a linkagedynamic model to construct a complete excavator model whichis much faster than a complete analytical model. Test resultsshow that the approach effectively captures the interactionsbetween the different actuators.I. IntroductionHydraulic machines are commonly used in the areas of con-struction, mining and excavation. A typical machine used fre-quently in excavation - a hydraulic excavator (HEX) - is shownin Fig 1. Today attention is being focused on automating taskssuch as mass excavation and continuous mining where a dig-ging machine fills a bucket with material from a pile or a rockface, transports the bucket load to a waiting truck or conveyerbelt, and dumps the load in the truckbed/belt. Such tasks areideal candidates for automation since they are repetitive andthere exists room for enhancing productivity.Fig. 1. A typical excavating machine (Hydraulic Excavator)BoomCylindersStick CylinderBucketCylinderSwing JointAutomation can be a practical reality only if the roboticmachine is more productive than a manually operated one. Thisrequires that tasks be performed optimally to minimize a com-bination of performance objectives such as time per bucketload and fuel consumption. Optimal motion computation inturn requires a robot model which defines the constraint surfacefor the path optimization problem. A complete robot modelconsists of an actuator model and a linkage dynamics model.While the linkage dynamics for an excavator robot can be mod-eled using the well-known Newton-Euler equations, the actua-tor model is rather complex and non-linear. The non-linearityis due to the highly non-linear hydraulic system, and also dueto the power coupling between the actuators, which are pow-ered by a limited power source (i.e. the engine). An analyticalactuator model for an excavator is therefore computationallyexpensive.This paper describes the construction of a fast hydraulic sys-tem and actuator model for an excavator through memory-based learning. The learned model has been used to construct acomplete excavator model which includes the second-orderlinkage dynamics in addition to the actuator model. This com-plete model is about an order of magnitude faster than a com-parable analytical model.The following notation will be used through the rest of thisdocument: “Linkage dynamic model” refers to the system ofNewton-Euler equations that describe the dynamics of theexcavator’s links, while an “actuator model” describes the actu-ator characteristics. The term “machine model” refers to a com-plete excavator model which includes both of the above.Although optimal motion planning can be performed withslower machine models, fast models raise the possibility of per-forming the optimal path computation as needed, even onboardthe robot, rather than pre-computing it off-line. An optimalmotion computation may require a few thousand evaluations/simulations, and the speed difference between a slow and a fastmodel could translate into the optimization taking a few daysversus a few hours.Fast machine models are also needed for collision avoidancethrough predictive simulation of motion commands before theyare executed. The expected trajectory through space can bescanned for collisions and the robot stopped in time in the eventof a predicted collision. (The use of predictive models is neces-sary when the masses are large and/or the velocities are highsince the dynamics of the system can make the response quitedifferent from a linear extrapolation of the velocity [5])The use of machine learning techniques to learn robotdynamics is not new. Neural networks that learn the dynamicequations of a robot manipulator ([2][3]) have been used inHydraulic System Modeling through Memory-based LearningMurali Krishna, John BaresThe Robotics InstituteCarnegie Mellon UniversityPittsburgh, PA - 15213model-based controllers. In [4] a neural network was used tolearn the error between an analytical dynamic model and actualmachine behavior during operation of the controller. Thislearned error function was used to improve controller perfor-mance. Although all the above cited researchers describe howneural networks improved controller performance, they do notdescribe how well the neural network learned the dynamicmodel. This is probably because their goal was to improve con-troller performance and not learn the dynamic model. In [8]McDonell et al. describe the construction of an analytical pneu-matic cylinder model, which was used to improve the controlby modelling the non-linearities inherent in pneumatic actua-tors. However, their pneumatic robot does not encounter anyflow limitations (and hence actuator interactions of the typeseen in a typical hydraulic machine) due the presence of a largeenough reservoir of high-pressure air.In [9] Singh et al. use a simple approach to handle the flowdistribution between multiple hydraulic cylinders on a hydrau-lic machine. They assume that the circuit with a valve closestto the pump gets all the flow it requires, and the remaining flowis distributed among the rest. This approach is valid when theinteracting cylinders have very different force loads, but notwhen the cylinders have similar force loads.The rest of the paper is organized as follows. Sec II gives abrief description of the structure of the equations involved in acomplete analytical model, to introduce the reader to the natureof such a problem. The following section (Sec III) describes thememory-based learning approach used to learn the actuatormodel. The results of the learning exercise are described inSec IV followed by some conclusions in
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