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XYY01-062@单注液压机液压系统设计,机械毕业设计全套
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附 录 A Fifth Motion and Vibration Conference, MOVIC 2000, Sydney, Australia, 4. - 8. December 2000 by University of Technology, Sydney SPEED-ADAPTED TRAJECTORIES IN THE CASE OF INSUFFICIENT YDRAULIC RESSURE FOR THE FOUR-LEGGED LARGE-SCALE WALKING VEHICLE ALDURO Daniel Germann, Jorg Muller and Manfred Hiller Gerhard-Mercator-Universitat GH Duisburg Fachgebiet Mechatronik, Lotharstrae 1, 47057 Duisburg, Germany Email: fgermann, mueller, hillergmechatronik.uni-duisburg.de ABSTRACT When operating walking machines, only a coordinated movement of all cylinders and/or motors can lead to safe, stable walking. The large hydraulically driven walking machine ALDURO, which is investigated in this paper, has no external power supply, and therefore the size of the on-board hydraulic power pack and its diesel engine is limited by its weight. When moving several cylinders with high speed, the hydraulic supply can become insufficient and the resulting trajectories of feet and platform can become unpredictable. When the ALDURO is near its stability limit such behaviour can lead to instability and toppling of the system. The proposed solution under discussion here is to observe the position errors and time derivatives for the cylinders and based on this reduce the speed when necessary. 1. INTRODUCTION The system investigated in this paper is the Anthropomorphically Legged and Wheeled Duisburg Robot (ALDURO). It consists of a platform of 2.0m by 2.2m with a cabin for the operator and four legs, each 1.8m long. The estimated weight is 1200 kg. It can be used as a quadruped walking machine (Fig. 2), and by replacing the two hind feet with wheels, it can also be used as a combined legged and wheeled vehicle (Fig. 1). The latter combines the advantages of a walking machine - high mobility - with the stability and speed of wheeled vehicles 2. When operating in steep and dangerous terrain, safety plays an important role. It must be guaranteed that the cylinders follow the calc ulated trajectories exactly since a wrong movement might cause the robot to nts become instable. ALDUROs legs are hydraulically driven, with an open hydraulic system. Normally, when planning hydraulic systems, low weight has no high priority 1. For the walking machine ALDURO the ratio power per weight was optimized. Fig. 1: Combined Legged Fig. 2: Walking Machine and Wheeled Vehicle While actuating several cylinders simultaneously or moving very fast, the volume flow of the hydraulic supply becomes insufficient and the resulting movements uncontrollable.The proposed solution under discussion here is a decrease in speed of all calculated trajectories. This is admissible as long as the robot is statically stable at any moment. By observing the position errors of the cylinders and their time derivatives, a decision is taken on whether to decrease or increase the speed along the trajectories. To ensure that all movements are influenced simultaneously, the model-time, upon which all calculations depend, is slowed down. Thus we can guarantee that legs and platform can and do follow the prescribed trajectories. This strategy is being tested on a virtual model of the ALDURO and is being tested on a virtual model of the ALDURO and a test stand in the laboratory,consisting of a single leg in scale 1:1, giving very good results. Fig. 3: Experimental setup 2. EXPERIMENTAL SETUP nts The leg of the ALDURO is anthropomorphic, i.e. it is based on the geometry and function of the human leg. The hip joint is a spherical ball joint with three degrees of freedom (d.o.f.) and the knee a revolute joint with one d.o.f. These joints are actuated with hydraulic cylinders (Fig. 4), whereas the two additional d.o.f. of the foot are passive. To make solution of the explicit inverse kinematics possible we lock one of the hip cylinders. The explicit solution of the direct and inverse kinematics is shown in detail in 4. To examine the dynamic behaviour of the leg, and to test different control schemes, an experimental setup for a fully sized leg was developed and built (see Fig. 3). It includes all the hydraulic components that will be used on the first prototype ALDURO and is driven by a stationary hydraulic power pack in the laboratory. The experimental set-up is equipped with an open hydraulic system with a 15kW electrical motor and an axial piston pump producing a volume flow of 40 l/min at 200 bar. This is smaller than what will be used on the real system, which will be powerd by a 27kW diesel engine. For tests with an insufficient hydraulic flow, a second set of four hydraulic cylinders (as used to move one leg) is mounted on the floor next to the test stand. An optical fieldbus for the transfer of the sensor and actuator data between the test stand and the control computer (with real-time operating system) is also installed. The hydraulic cylinders include position and pressure sensors that are used as controller inputs. Thus dynamic tests can be carried out to examine the co-operation between the mechanical and hydraulic components and the electronic control system. The hip plate of the experimental set-up is mounted on a pair of linear bearings, and thus is mobile in vertical direction. When combined with the foot, as shown in Fig. 3, or the passive wheel used on the hind leg of the combined legged and wheeled system, this allows loading tests on the leg while performing walking motions. Mechanical stops below the hip plate allow the foot to be lifted in the swing phase of the walking motion. The first (unloaded) tests have shown the mobility of the anthropomorphic leg mechanism to be very good, and the optical fieldbus system has also proven to be reliable. nts 3. SPEED ADAPTATION 3.1 Insufficient Hydraulic Flow As already mentioned, the weight and size of the onboard power pack is limited and has to be kept low. When moving several cylinders simultaneously or with a high speed the hydraulic supply can become insufficient and the pressure will collapse. In this case the resulting movement depends mainly on the sizes of the proportional valves and external loads on the cylinders. The trajectories of the feet and platform become erratic. When ALDURO is near limit of its stability such behaviors can lead to instability and toppling of the system. As the safety issue is a very important one (people could be harmed) this pressure collapse has to be prevented. To investigate this behavior, a circular movement (radius 0.2 m, velocity 0.5 m/s) of the foot in the horizontal plane 1m below the hip was chosen as a reference. This trajectory has the advantage that it actuates all three unlocked cylinders. With a typical vertical stepping movement of the foot the sideways cylinder (no. 2 in Fig. 4) is nearly stationary. The inverse kinematics for the mapping of the foot co-ordinate into the co-ordinate space for the three cylinders has been developed in the C+ programming environment Ma a a aBILE 3. nts When implemented on the test stand the resulting trajectory of the foot degenerated to a rounded rectangle (Fig. 5). To increase the hydraulic consumption, both sets of hydraulic cylinders have been used (i.e. leg cylinders and set of four cylinders on the ground). As we can see in Fig. 6, cylinder no. 2 lags far behind its sinusoidal set-point curve. The linear movement of the cylinder indicates a fully open proportional valve. The available hydraulic volume flow is clearly insufficient. 3.2 Trajectory Speed Reduction The problem of uncontrollable movements can be approached from different directions: Redimensioning of pump and valves, Predict insufficient flow/pressure with detailed model of hydraulics and recalculate nts critical movements with lower velocities, Detect position errors due to pressure drop and slow down all movements, while maintaining trajectories. The first approach increases the weight of the hydraulic system and is thus undesirable. The second is undesirable because of computing power required and inaccuracy in the hydraulic model. Therefore, detection of the position error and slowing down the movement was chosen and implemented here. Instead of recalculating all trajectories for the case of a necessary deceleration, the time variable on which all trajectories depend is slowed down. To this end a new time variable is introduced. This trajectory time or model time t* can be expressed as a function of realtime t and the error dependent factor for the time increment All trajectories are functions of this t* For the control system running on a real time operating system we need the discrete relationship between t and t* for time step i. As all trajectories are functions of t* they will all be simultaneously slowed down or sped up, depending on k mt; i. As an indicator for insufficient hydraulic flow, a function of the position errors of the cylinders is chosen. The vector s j contains the set-point positions for the cylinders in each leg and i j the vector of measured positions. The difference is the error in meters. Where fl stands for front left, hr for hind right and so forth. With the weight matrix W, the influence of the four cylinders in each leg on the foot position can be adjusted. nts We take the normalized weighed sum of the squares of the errors for all cylinders e and its first time derivation de and normalize both with the admissible errors (thresholds e thr and de thr). If the sum of e and de exceeds the upper limit, the model time is slowed down. As both e and de are normalized with a threshold, this upper limit can be fixed. In this case it is 2. The third threshold (lower limit) is used to decide when to increase the speed again. To prevent a decrease in error triggering a stop in deceleration or even an acceleration, even if the error is still too large, de is only added if it is positive. where k mt,dec is the rate of change of k mt for deceleration and k mt,acc is the same for acceleration. K mt has to stay inside the limit k mt,min 1. 3.3 Results Values for thresholds, acceleration and decelerationrates of model time and cylinder weights are set empirically. The cylinders at the hip joint have a higher influence on the foot position than cylinder no. 4 at the knee. The corresponding weighing is set to 2:1. As the system has to react very quickly to errors,the deceleration rate k mt,dec is high. To prevent too much oscillation, the acceleration rate k mt,acc is set lower than k mt,dec. nts Fig. 7: Cylinder positions for speed adapted trajectory In Fig. 7, at t = 2.5 s we can see the set-point value for cylinder 2 rising fast, and that it cannot be followed by the physical system. The resulting normalized error can be seen in Fig. 8, where it oversteps the threshold e thr,2 and triggers the deceleration of the model time t* by decreasing the model time factor k mt (as seen in Fig. 9.) By setting the thresholds e thr and de thr the influence of the absolute error and the change in error can be adjusted. As the latter is a time derivative of a measured signal it is likely to be noisy. Here this threshold is set low. Another possibility would be to filter the signal with the disadvantage that this would produce a larger dead band. nts 4. CONCLUSIONS Due to high safety demands for the operator driven walking machine ALDURO, the need arises to guarantee actuator movements are executed exactly as calculated by the controller. With all actuators moving simultaneously or at high speed the hydraulic supply can become insufficient and the pressure can collapse.The method described here to prevent this is based on detecting deficiencies in the hydraulic flow by observing the position errors at the actuators and slowing down all movements if necessary. The implementation of an adjustable model time for the calculation of trajectories on the test leg from ALDURO looks promising. The execution of movements at high velocity has been improved drastically. 5. FUTURE WORK nts At the moment the controller for the leg is a proportional controller with inputs from the inverse kinematics and with one cylinder locked. To be able to use all cylinders and to reduce the tracking errors this controller will be replaced with a force and model based controller. This should reduce the remaining position errors as shown in Fig. 10. Signals from additional pressure sensors in the hydraulic circuit will be included in the evaluation of the hydraulic power supply. 6. ACKNOWLEDGEMENT This work is substantially supported by the Deutsche Forschungs gemeins -chaft DFG (German ResearchCouncil.) REFERENCES 附 录 B nts 如何为大型的步行机器人在供能不足的情况下 选择合适的速度轨道 摘 要 在操作步行机器人时，只有让所有的油缸协调动作，才能使之安全、稳定的行走。本文所研究的这个大型液力驱动步行机器人 ALDURO 并没有外部力量的供给。因此，在机器人平台上的液压装置及其柴油引擎的尺寸大小都将被它们自身的重量所限制。当各个油缸以高速运动时，液压 力的供给就将不足，从而导致机器人的脚步及其整个平台的移动轨迹都将变成不可预知的。当此 ALDURO 在接近其稳定边界的状态运作就将导致它的不安定甚至是整个系统的瓦解，下面将讨论的解决方案是用于发现这种油缸时位错误并由此在需要的时候降速。 1、介绍 本文中所研究的系统是像人一样的可以用脚行走但又可以有轮子的机器人 ALDURO。它是由一个其上有一间为操作人员所准备的小屋的平台和四只每只长为 1.8 米的脚所组成。估计它的重量是 1200公斤。它可以被用作是像四足动物一样行走的步行机器（如图 2），而且当将其后面的两只脚用轮 子替换时，它又能被当作是一种有腿有轮的，腿和轮相结合的交通工具（如图 1），现今的这种腿和轮相结合的步行机相对于那种全部是轮子的交通工具的稳定性和速度而言，其优势在于它高度的机动性 2。 Fig. 1: Combined Legged Fig. 2: Walking Machine and Wheeled Vehicle 当在险峻及危险的地带操作时，安全扮演了重要的角色。只要在移动中出现了一个错误，机器人都将可能变的不稳定，因此，机器人的气缸必须确保要完 全地按计划轨道动作。步行机器人的腿是籍由一个开启了的液压系统所提给的液力驱动的。正常地情况下，在设计这种液压系统时，优先考虑重量最大的部分。而对于这个步行机 ALDURO，它每一处的比值都是被最优化了的。 一旦同时发动了多个气缸或气缸的运动速度非常快时，由液压所供给的流量就将变的不足，从而导致机器人的运动变得无法控制。下面所讨论到的解决方案是关于计算轨道上速度如何减少的，机器人要随时都可以稳定的停下来。籍由发现那些气缸的时位错误，并由此作出在轨道上减速或者增速的决定，运动同时被触发，所有计算所依赖的采样频率将 被降低，如此我们便可以保证机器人的腿以及它的平台能且确实随着预定的轨道运行。这个策略可以被应用于 ALDURO 的虚拟模型的测试中并且正在实验室中被应用。 nts Fig. 3: Experimental setup 2、实验的装备 ALDURO 的腿是拟人的 ， 也就是说它是以几何学和人类的腿的功能为基础的。它的股关节是一个自由度为三的圆球形的球接头，它的膝部是一个只有一个自由度的涡形的接头。这些接头的动作都是由液压缸驱动的（如图 4）。然而，它脚上所附加的两个自由度对它而言，作用却是消极的，为了使得到一套明确的翻转运 动学的方案变成可能，我们锁上了股关节处的一个液压缸。这个直接的翻转运动学的明确的方案详细的显示在 4上。 为了调查腿的动态行为，并测试不同的控制方案，一种专为一只完全按规定尺寸制作的腿而设计的实验装置发展，并被制造出来了（如图 3）。 它包括所有将在实验室中被用于第一台 ALDURO原型的液压装置及由液压力稳定驱动的装置。这个实验装置上由一个拥有一个 15kw的电动机和一个流量为40l/min的柱塞泵的液压系统所构成。这比起真的系统中所使用的 27kw的柴油引擎可要小的多了。为了测试液压流的不够，另外的四个液压缸（ 被看做是一只脚）被安在试验支架的边上。 一个用来实现测试支架传感器内容和控制计算机（有一个即时操作系统）数据转换的光学线路也被安装使用了。液压缸就被当作是包括了位置和压力感应器的输入装置使用。因此，这种动态的测试就可以在机械、液压组件和电子控制系统三者互相结合的情况下被实行。 实验装置的臀部是安装一对线形 轴承上，因此，它在垂直方向上是可移动的。 不管是像图 3那样脚的组合，还是在腿和轮结合的系统中用轮子装在两只后脚上，当步行运动进行时在其腿上的测试都将被允许载入。在行走过程中那种 摇摇摆摆着把臀不以下的脚抬起来的 行动被停止下来。 这第一次的测试很好的显示了模拟人腿的机械装置的灵活性，并且这里的光学总线系统也已经被证明了是可靠的。 nts 3、加速改编 3.1 不足的液压流量 正如已经提到的，在面板上那些能量供应包因为自身的重量和尺寸的被限制而不得不保持底下。 当多的液压缸同时运动或当它们以高速运行时，液压力是供给将会不足而且系统的压力也会匮乏。 这 种 情况产生的运动主要地依靠阀比例的大小和液压缸的外部的负荷。 它的脚和平台的轨迹就将是杂乱无章的。 当 ALDURO 接近系统的稳定性的界限时这样的 行为能导致不稳定甚至推翻原来稳定的系统。同样非常重要的安全问题是必须 防止压力的崩溃 (人们将会受到伤害 )。 为了要研究这种情况 , 叁考在水平的状态下在臀部下面 1 m的脚平面上做一次圆形的运动 (半径 0.2 m,速度 0.5 m/s)。这一个轨道的形成要有三个开启的液压缸作用。而脚的一次典型的垂直步进运动它旁边的液压缸 (图 4 的 2 号 ) 几乎是不动的。像三个液压缸驱动脚的旋转映射出的在空间中的旋转的运动学为已经在 C+设计环境中得到了发展 3。 当在试验支架上进行实验时引起脚的轨道退化到一个封闭矩 形时 .(图 5) 为了要增加液压的消耗 ,液压缸的组合就会被使用 (也就是脚上的液压缸即四个固定组合在地面上的液压缸 ). nts 正如我们能在图 6 中所看到的那样 ,2 号缸远远滞后于在它的正弦曲线。液压缸的线性运动显示出一个完全开启着的定量阀。可利用的液压流量明显不够。 3.2 轨道速度减少 无法控制其运动的问题可以从不同的几个方面着手处理 : 改变泵和阀的尺寸。 通过 详细的模型
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