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Development of a walking machine: mechanicaldesign and control problemsTeresa Zielinska *, John HengAbstractThis paper describes: a novel design of the leg drive mechanism, hardware architecture andthe leg control method for a walking machine being developed to study various walking gaitstrategies. The leg mechanism employs an inverse differential gear drive system providing largeleg lift and swing sweep angle about a common pivotal point while being driven collectively bya pair of motors. The development platform consists of a pair of legs mounted adjacently toeach other on a linear slide. A three-axis piezo transducer is mounted on the feet to measurethe various vector forces in the legs during the support phase. The force sensing results arepresented and discussed. Currently one small four-legged prototype and one hexapod are usedfor the tests of different gait patterns. _ 2002 Elsevier Science Ltd. All rights reserved.Keywords: Walking machines; Mechanical design; Control system design; Force sensing1. IntroductionIn comparison with the industrial manipulators, the task of building an adaptable,autonomous walking machine is more difficult. Walking machines have moreactive degrees of freedom (DOF) than industrial robots. To enlarge the work-spaceof the leg-end, and thus enhance the machines ability to adapt to the terrain, each leg should have at least three DOF, which results in a total of 12 DOF for a quadrupedor 18 DOF for a hexapod. All those joints must be controlled adequately in realtime. This also means that the hardware and software systems must meet more criticalrequirements than those formulated for industrial robot controllers. Moreover, fullyautonomous vehicles use only on-board controllers and so those controllers have tobe miniaturized to an utmost extent. There is no such requirement in the case of nonmobilecontrollers of manipulators. Theoretical problems that must be solved arenumerous. From an overview of the publications concerning the subject of multileggedwalking machines it can be noticed that the main attention is paid to: general (technical) description of prototypes, e.g., 1, methods of free gait planning, e.g., 2,3, problems of gait synthesis using dynamical or quasi-dynamical modelling, (e.g.,force distribution problems) 47, the problems of motion optimization 8,9, the philosophy of control systems functional decomposition and mechanisms ofmachines adaptive behavior 10,11.The description of control software component is lacking. Such a descriptionis necessary in the systematic development of walking machines, which should betreated as mechatronic systems.Mechanical structure of a walking machine should not only imitate the leg structureof living creatures (e.g., insects, spiders), but should also take into account theactuating systems properties (e.g., size, weight and power of the motors) and constraints(e.g., size of the body and the leg work-space).Fig. 1. LAVA using the multipurpose leg being developed at RRC (Robotics Research Centre NanyangTechnological University, Singapore).In this paper, we are presenting the mechanical structure of a multilegged machineand we are giving a brief description of joint, leg and gait levels of the controlsystem.2. Mechanical design2.1. Mechanical problemsThe need for a general solution to the problem of robot legs design, that can beused either by two-, four- or six-legged vehicles, is clear. However the ability to meetthis need has been hampered by the lack of adequate joint mechanisms and controls.Joint technology is a key problem in the development of such vehicles, because hipand ankle joints require, at a minimum, pitch and yaw motion about a commoncenter with remote location of actuation sources analogous to our muscles and joints.The lack of simple, compact, cost-effective and reliable actuator packages has alsobeen a major stumbling block in current designs. Ineffective joint design leads tounwieldy vehicles that compensate for the instability of their simple joints by meansof additional legs.2.2. Unique differential leg mechanismThe general structure of a walking machine legged autonomous vehicular agent(LAVA) 12,13 is shown in Fig. 1. The thigh section employs a differential gear drivesystem to achieve both leg swing and leg lift functions (Fig. 2). This drive systemoffers two distinct features that are superior to conventional leg design. Firstly, leglift and leg swing functions operate from a common geometrical pivot point. Thisfeature will prove beneficial when performing workspace and kinematic modeling.Secondly during leg swing and leg lift motions, both motors are constantly workingtogether to achieve the desired motion. No motor is left idle and so is not carriedaround as a dead weight, when only one particular leg motion is in use. The advantagewould be that two smaller lighter motors can be utilized which can becombined to provide a cooperative effort instead of the conventional independentmotor drive design. The result would provide savings in power consumption, weightpenalty and size constraints. Other power-saving features include using worm gearsat a particular gear ratio to drive the various appendages. This provides a self-lockfeature thus removing the need to keep the motors continuously powered whenholding the walking machine at a particular orientation. To provide maximum footplacement flexibility with precise turning functions, full three DOF were incorporatedinto each leg.2.3. Fully invertable walking machine platform with amphibious adaptabilityThe large leg lift and swing angle complements the symmetrical leg design, whichenables the walking machine to be invertable. This feature is seen as being essential,Fig. 2. The differential gear drive systemif the walking machine is to operate within the surf zone of a seashore. The absenceof awkwardly exposed mechanical drive systems allows the walking machine to beeconomically water isolated and hence obtains amphibious capability. The walkingmachine can be configured to walk on the sea bed or spread its limbs to increasebuoyancy and hence swim on the surface (Fig. 3).2.4. Convertible to insect/mammalian configuration with segmentable leg pairThe wide leg lift and swing capability allow the modular leg to be adapted foruse in either an insect or mammalian leg configuration (Fig. 4). Utilizing the leg inmammalian configuration requires only a small adjustment to the leg geometry. Theadded benefit of having a wide leg lift and swing capability is that the front two legscan be adapted to perform probing or pick and place functions (Fig. 5). The modularFig. 3. The walking machine in swimming mode.Fig. 4. Configuration of LAVAs legs: (a) insect leg configuration; (b) mammalian leg configuration.leg can be adapted to a four- or six-legged vehicle or employed in an omnidirectionalhexapod configuration.2.5. ConclusionThe modular approach followed in the leg development offers several additionalbenefits. The thigh and lower leg length can be adjusted quickly to assume differentleg length requirements. There is free space in the central column of the leg to accommodatevarious sensors, data and power cables. The current implementation ofthe leg design can accommodate two different gear ratios for differential gear driveunits. If an increase in drive motor power is required in the future, only minormodifications are required to accommodate the bigger motors. Similarly, leg supportingbeams can economically be resized by changing geometrically simple components.Finally, with a large leg lift and swing angle the walking machine can bemanipulated in a prone mode to operate in restrictive spaces or be neatly foldedfor easy storage or deployment (Fig. 6). The leg servo drive actuator system is designedaround a modified differential gear system thus allowing large leg lift andswing motions to be achieved about the same pivotal point thus providing simplerleg geometry than conventional leg designs.Fig. 5. Pick and place option.3. Control system3.1. Functional decompositionThe functional structure of the control software was decomposed into hierarchicallyrelated levels (Fig. 7). The lowest level includes joint control. The angularjoint positions are evaluated from the leg-end trajectory shape defined in Cartesianspace. Inverse kinematics model is implemented there to evaluate the joint angularpositions. Incremental rotary optical encoders mounted on motor shafts are usedas the feedback devices. The motor controllers use the PID algorithm to computethe angular positions. In the solution of inverse kinematics, simple singularities andproblems of non-unique choices of configurations were considered.The upper level leg level produces the leg-end trajectory according to the propertiming scheme. The next level is the gait level. The rhythmic and free gait will begenerated by it. In the case of pick and place operations, this level will also generatetrajectories of front legs treated as manipulators. The uppermost level of the controlsoftware will be responsible for the generation of the body (body level) trajectoriesaccording to the user commands or according to the sensory readings. For the gaitand body level, the most serious problem is to elaborate the method of free gaitgeneration taking into account that there are obstacles of different size and density,which must be avoided 16. It was assumed that motion planning must be donein real time (neither the leg-end trajectory is pre-planned nor the sequence of legsFig. 6. Lava leg position: (a) prone configuration; (b) folded configurationtransfers is fixed). The transition from one state to another is performed taking intoaccount: stability conditions, sensory readings, goal of machine motion and leg-endcoordinates of other legs. Free gait must be statically stable, i.e., projection of vehiclecenter of gravity must be inside the support polygon. The planning of free gait isexecuted in parallel for all the legs. This includes two planning phases in analogy tothe motion planning done by human brain 14.Force-control feedback is included in the leg level of the controller functionalstructure. After simulation tests, the hybrid force-control algorithm (based on activecompliance force-control method) was chosen as a simple and effective controlmethod. Force control is made along the directions in which the leg-end is constrainedby the environment (direction normal to the ground level) and pure positioncontrol is executed along the other directions, in which the leg is unconstrained andso free to move.3.2. Structure of the hardware system and general properties of the softwareThe hardware structure of control system (Fig. 8) includes: PC host (leg CPU),motion control cards (PID controllers) connected to the amplifiers powering the legmotors. To provide position feedback, 16-bit digital encoders are used. Leg-endthree-component KISTLER piezoelectric force sensor coupled through a 4-channelcharge amplifier to an A/D converter that delivers the data to the PC host.The control cards use National Semiconductor LM680 dedicated motion-controlprocessors. Controllers are treated as bus peripherals and are programmed by thehost computer. Sampling rate (time necessary to obtain the encoder readings, computethe set values and attain them) depends on the motor control method (PWM orvoltage control) to a minor extent. In our case of voltage control is used and so thesampling rate is in the range of 400 ls. The time of one micro-step (on the leg level)can be chosen depending on the motion properties. It was found out by variousexperiments, that this time cannot be shorter than 0.03 s for smooth leg-end movementin the short transfer phase with the support phase being two/three times longer.Controllers use trapezoidal velocity profile for motor motion (the so-called positionmode). Adequate procedures are responsible for calculating maximum velocity and acceleration for each micro-step. During trajectory following motion, to prevent legendvibrations, the acceleration must be constant. Proper values of acceleration wereobtained experimentally for each motor separately. Those values are different forthe leg-end transfer phase and for the support phase. The programmer is responsiblefor proper evaluation of acceleration and velocity. Errors in those calculations candestroy the motion time scheme, and that can result in motor shaft vibrations. Forthe point-to-point motion it was assumed that the time of one micro-step is long 4 swhen compared with 0.03 s in continuous path motion. One-sixth of this time,motors should accelerate, next 4/6 of micro-step motor speed should be constant andnext one-sixth motor must decelerate (Fig. 9). It was tested by experiments that forthese values and for every possible range of movement inside the work-space thecalculated acceleration and velocity is never above the maximum range.If the number of samples for one micro-step is equal to n, and the distance thatmust be traversed is equal to Ds (in increments) the velocity v must be equal to For the trajectory following movement, motor acceleration should be constant (forsmooth leg-end movement). In this case, to reach every possible reference positionduring the fixed micro-step the time the acceleration/deceleration must beflexible and velocity must be calculated adequately. Assuming that unknown accelerationtime (expressed in sampling periods) is equal to the deceleration time andis denoted by x, we can find that the change of position during n samples is equal From the above, to calculate that the total acceleration and deceleration time xmust be less than half of the time necessary for the execution of one micro-step, sowe have Analyzing the above relation, it is easy to find that the acceleration must be greaterthan a certain value to prevent having as a solution an unrealistic complex number.On the other hand, the acceleration cannot be too big, which means very short ac-Fig. 10. Inter-process communication.celeration/deceleration time and rapid motor motions. Assuming that this time mustbe longer than 1/12 of the micro-step we findDistance increment Ds can vary considerably. For this reason it is difficult to calculatethe acceleration using only (5). In practice the proper value of acceleration wasfound experimentally, but paying attention to (5). For experimental evaluation of a,many motions were observed while monitoring the values Ds the extreme values ofacceleration when the fixed velocity profile (rel. (1), (2) was used. Later, considering(5), acceleration was fixed separately for the leg-end transfer and for the supportphase. Transfer phase is usually much shorter than the support phase.3.3. Real-time control systemThe motion card commands are transmitted from a program running on the host.The real time QNX operating system and Watcom C are being used in the developmentof the control software. The inter-process cooperation is according to thetypical clientserver pattern. Currently three processes have been developed intosoftware: leg process, driver process and sensor process. The leg process is the clientwhile both the sensor and driver processes are the servers. The leg process is responsiblefor the generation of motion trajectories according to the rules given bya programmer and the data received from the sensor process. Sensor process servesforce sensor. The driver process is responsible for the cooperation with hardware. Itreceives command and data from the leg process, transforms that data to the formatacceptable by hardware (motion controllers) and communicates with the hardware.The back-paths (from servers to clients) include the transmission of: sensor data(from sensor process), confirmations of the end of movement (from driver process)and, information about the errors which can be hardware or software type (Fig. 10).The leg process user (programmer) defines different shapes of leg-end trajectoryfor continuous path motion or sends only coordinates of the final position (positionof leg-end or angular joint position) for the point-to-point motion. Programmeris responsible for manual synchronization of the legs (from PC hostkeyboard). In the design of control software it was assumed that, in the future,control program would be implemented in an autonomous on-board control computer.4. Force sensing4.1. IntroductionForce control is needed to increase the ability of the machine to adapt to irregularterrain and to different types of soils. In locomotion over complex terrain, a necessitymay arise to control the horizontal force components, so that contact forces areT. Zielinska, J. Heng / Mechatronics 12 (2002) 737754 747within friction cones. In locomotion over soft soil, it is necessary to control the legloads because of their sinking into the soil. In locomotion over slightly uneven terrain,the extent to which a leg sinks can be determined taking into account leg jointspositions, readings from the inclinometers and load on the legs determined by theleg-end force sensors.The simplest way to walk on soft soil is to use fixed locomotion cycles. Howevernon-homogeneity of the soil mechanical properties and unevenness of the terrainmay result in noticeable disturbances of machine motion. To obtain a smooth motion,there is a need to individually correct the motion of each leg in taking intoaccount the distance by which it sinks into the ground. In the simpler case where thesoil properties a