Hydraulic System Modeling through Memory based Learning Murali Krishna John Bares The Robotics Institute Carnegie Mellon University Pittsburgh PA 15213 Abstract Hydraulic machines used in a number of applications are highly non linear systems Besides the dynamic coupling between the different links there are significant actuator nonlinearities due to the inherent properties of the hydraulic system Automation of such machines requires the robotic machine to be atleast as productive as a manually operated machine which in turn make the case for performing tasks optimally with respect to an objective function say composed of a combination of time and fuel usage Optimal path computation requires fast machine models in order to be practically usable This work examines the use of memory based learning in constructing the model of a 25 ton hydraulic excavator The learned actuator model is used in conjunction with a linkage dynamic model to construct a complete excavator model which is much faster than a complete analytical model Test results show that the approach effectively captures the interactions between the different actuators I Introduction Hydraulic machines are commonly used in the areas of construction mining and excavation A typical machine used frequently in excavation a hydraulic excavator HEX is shown in Fig 1 Today attention is being focused on automating tasks such as mass excavation and continuous mining where a digging machine fills a bucket with material from a pile or a rock face transports the bucket load to a waiting truck or conveyer belt and dumps the load in the truckbed belt Such tasks are ideal candidates for automation since they are repetitive and there exists room for enhancing productivity Swing Joint Stick Cylinder Bucket Cylinder Boom Cylinders Fig 1 A typical excavating machine Hydraulic Excavator Automation can be a practical reality only if the robotic machine is more productive than a manually operated one This requires that tasks be performed optimally to minimize a combination of performance objectives such as time per bucket load and fuel consumption Optimal motion computation in turn requires a robot model which defines the constraint surface for the path optimization problem A complete robot model consists of an actuator model and a linkage dynamics model While the linkage dynamics for an excavator robot can be modeled using the well known Newton Euler equations the actuator model is rather complex and non linear The non linearity is due to the highly non linear hydraulic system and also due to the power coupling between the actuators which are powered by a limited power source i e the engine An analytical actuator model for an excavator is therefore computationally expensive This paper describes the construction of a fast hydraulic system and actuator model for an excavator through memorybased learning The learned model has been used to construct a complete excavator model which includes the second order linkage dynamics in addition to the actuator model This complete model is about an order of magnitude faster than a comparable analytical model The following notation will be used through the rest of this document Linkage dynamic model refers to the system of Newton Euler equations that describe the dynamics of the excavator s links while an actuator model describes the actuator characteristics The term machine model refers to a complete excavator model which includes both of the above Although optimal motion planning can be performed with slower machine models fast models raise the possibility of performing the optimal path computation as needed even onboard the robot rather than pre computing it off line An optimal motion computation may require a few thousand evaluations simulations and the speed difference between a slow and a fast model could translate into the optimization taking a few days versus a few hours Fast machine models are also needed for collision avoidance through predictive simulation of motion commands before they are executed The expected trajectory through space can be scanned for collisions and the robot stopped in time in the event of a predicted collision The use of predictive models is necessary when the masses are large and or the velocities are high since the dynamics of the system can make the response quite different from a linear extrapolation of the velocity 5 The use of machine learning techniques to learn robot dynamics is not new Neural networks that learn the dynamic equations of a robot manipulator 2 3 have been used in To be presented at the IEEE Intelligent Robot Systems Conference IROS Victoria B C Canada October 1998 model based controllers In 4 a neural network was used to learn the error between an analytical dynamic model and actual machine behavior during operation of the controller This learned error function was used to improve controller performance Although all the above cited researchers describe how neural networks improved controller performance they do not describe how well the neural network learned the dynamic model This is probably because their goal was to improve controller performance and not learn the dynamic model In 8 McDonell et al describe the construction of an analytical pneumatic cylinder model which was used to improve the control by modelling the non linearities inherent in pneumatic actuators However their pneumatic robot does not encounter any flow limitations and hence actuator interactions of the type seen in a typical hydraulic machine due the presence of a large enough reservoir of high pressure air In 9 Singh et al use a simple approach to handle the flow distribution between multiple hydraulic cylinders on a hydraulic machine They assume that the circuit with a valve closest to the pump gets all the flow it requires and the remaining flow is distributed among the rest This approach is valid when the interacting cylinders have very different force loads but not when the cylinders have similar force loads The rest of the paper is organized as follows Sec II gives a brief description of the structure of the equations involved in a complete analytical model to introduce the reader to the nature of such a problem The following section Sec III describes the memory based learning approach used to learn the actuator model The results of the learning exercise are described in Sec IV followed by some conclusions in Sec V II Problem background The testbed used for the work
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