Development of a walking machine: mechanicaldesign and control problemsTeresa Zielinska *, John HengAbstractThis paper describes: a novel design of the leg drive mechanism, hardware architecture and the leg control method for a walking machine being developed to study various walking gait strategies. 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 measure the 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 used for 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-space of the leg-end, and thus enhance the machine’s ability to adapt to the terrain, each leg should have at least three DOF, which results in a total of 12 DOF for a quadruped or 18 DOF for a hexapod. All those joints must be controlled adequately in real time. This also means that the hardware and software systems must meet more critical requirements than those formulated for industrial robot controllers. Moreover, fullyautonomous vehicles use only on-board controllers and so those controllers have to be 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 multilegged walking 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) – [4–7],• the problems of motion optimization – [8,9],• the philosophy of control systems functional decomposition and mechanisms of machines’ 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 be treated as mechatronic systems.Mechanical structure of a walking machine should not only imitate the leg structure of living creatures (e.g., insects, spiders), but should also take into account the actuating 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 themultipurpose leg beingdeveloped at RRC (RoboticsResearch Centre – NanyangTechnologicalUniversity, Singapore).In this paper, weare presenting themechanical structureof a multileggedmachineand we are giving abrief 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 be used 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 hip and 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 also been a major stumbling block in current designs. Ineffective joint design leads to unwieldy vehicles that compensate for the instability of their simple joints by means of 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 system offers two distinct features that are superior to conventional leg design. Firstly, leglift and leg swing functions operate from a common geometrical pivot point. This feature will prove beneficial when performing workspace and kinematic modeling.Secondly during leg swing and leg lift motions, both motors are constantly working together to achieve the desired motion. No motor is left idle and so is not carried around as a dead weight, when only one particular leg motion is in use. The advantage would be that two smaller lighter motors can be utilized which can becombined to provide a cooperative effort instead of the conventional independent motor drive design. The result would provide savings in power consumption, weight penalty and size constraints. Other power-saving features include using worm gears at a particular gear ratio to drive the various appendages. This provides a self-lock feature thus removing the need to keep the motors continuously powered whenholding the walking machine at a particular orientation. To provide maximum foot placement 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, which enables 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 absence of awkwardly exposed mechanical drive systems allows the walking machine to be economically ‘‘water isolated’’ and hence obtains amphibious capability. The walkingmachine can be configured to walk on the sea bed or spread its limbs to increase buoyancy 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 for use in either an insect or mammalian leg configuration (Fig. 4). Utilizing the leg inmammalian configuration requires only a small adjustment to the leg geometry. The added 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 LAVA’s legs: (a) insect leg configuration; (b) mammalian leg configuration.leg can be adapted to a four- or six-legged vehicle or employed in an omnidirectional hexapod 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 different leg 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 drive units. If an increase in drive motor power is required in the future, only minor modifications 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 simpler leg 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 hierarchically related levels (Fig. 7). The lowest level includes joint control. The angular joint positions are evaluated from the leg-end trajectory shape defined in Cartesian space. Inverse kinematics model is implemented there to evaluate the joint angular positions. Incremental rotary optical encoders mounted on motor shafts are used as 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 proper timing 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) trajectories according to the user commands or according to the sensory readings. For the gait and body level, the most serious problem is to elaborate the method of free gait generation 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 done in 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-end coordinates of other legs. Free gait must be statically stable, i.e., projectionof vehiclecenter of gravity must be inside the support polygon. The planning of free gait is executed 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 functional structure. After simulation tests, the hybrid force-control algorithm (based on activecompliance force-control method) was chosen as a simple and effective control method. 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 leg motors. To provide position feedback, 16-bit digital encoders are used. Leg-end three-component KISTLER piezoelectric force sensor coupled through a 4-channel charge 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 the host computer. Sampling rate (time necessary to obtain the encoder readings, compute the 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 various experiments, that this time cannot be shorter than 0.03 s for smooth leg-end movement in 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 legend vibrations, the acceleration must be constant. Proper values of acceleration were obtained experimentally – for each motor separately. Those values are different forthe leg-end transfer phase and for the support phase. The programmer is responsible for proper evaluation of acceleration and velocity. Errors in those calculations candestroy the motion time scheme, and that can result in motor shaft vibrations. For the 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 and next 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 the calculated 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 that must 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 (for smooth leg-end movement). In this case, to reach every possible reference position during 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 – x must 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 must be 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 was found experimentally, but paying attention to (5). For experimental evaluation of a,many motions were observed while monitoring the values Ds – the extreme values of acceleration 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 development of the control software. The inter-process cooperation is according to thetypical client–server pattern. Currently three processes have been developed into software: leg process, driver process and sensor process. The leg process is theclientwhile 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 format acceptable 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 trajectory for ‘‘continuous path’’ motion or sends only coordinates of the final position (positionof leg-end or angular joint position) for the ‘‘point-to-point’’ motion. Programmer is 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 irregular terrain and to different types of soils. In locomotion over complex terrain, a necessitymay arise to control the horizontal force components, so that contact forces are T. Zielinska, J. Heng / Mechatronics 12 (2002) 737–754 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 joints positions, readings from the inclinometers and load on the legs determined by the leg-end force sensors.The simplest way to walk on soft soil is to use fixed locomotion cycles. However non-homogeneity of the soil mechanical properties and unevenness of the terrain may 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 into account the distance by which it sinks into the ground. In the simpler case where thesoil properties are known, the correction of leg-end position can be computed on thebasis of the commanded force, without badly affecting the quality of motion. There isthe need to consider the amount of sinking and to solve the problem of proper legload distribution, if the soil properties are not known or the terrain is uneven [2].Force-controlled walking machine would give additional advantages by increasing energy efficiency by reducing the internal forces between legs and providing the desired support forces regardless of the behavior of the terrain threaded on. WeFig. 11. Test rig of two prototype LAVA legs with three-component piezoelectric force sensor and top view of one two-legs module.know that the accuracy attained in (for example) industrial robots is not needed inwalking machines nor is it economically viable. Low ability to adapt to the environmentis a problem of position control. A position-controlled leg of a walkingmachine would either move in the air without exerting any forces on the body or exert all the forces available in the case of an uneven terrain. The latter possibilityhappens if there is a position error (due the lack of proper environment model, due to the control method or due to the change of environment properties). Let us assumea case when a stone gets stuck between two legs, they would press it betweenthem relatively hard under position control. How hard, depends on the compliance of the position control of the legs. This is not the case under force control, where thepressing force would be commanded by one and is typically very small between two legs. Minimizing the forces in the ground plane directions offers the chance toreducethe possibility of slipping of a leg on the ground [2].5. SummarySystematic approach to mechanical and control system design can introduce into it flexibility that is necessary for future development and modifications.In this paper, a novel design of the leg actuation mechanism was described. It was characterized by multiple configurations in which the leg could be utilized and large leg lift and swing angles. General suggestions regarding the control software development are also presented. Results of experimental work on joint/leg level controller are discussed. The advantages of force sensing for synthesizing the walking machine motion are shown. Appropriate experimental results are presented.AcknowledgementsThis work was conducted with the support of Robotics Research Center,Nanyang Technological University, Singapore.References[1] Pugh RD, Ribble EA, Vohnout VJ, Bihari TE, Walliser TM, Patterson MR, Waldron KJ. Technicaldescription of the adaptive suspension vehicle. Int J Robotics Res 1990;9(2):24–42.[2] Hartikainen K. Motion planning of a walking platform designed to locomote on natural terrain.Helsinki: Helsinki University of Technology; 1996.[3] Pal PK, Jayarajan K. Generation of free fait – a graph search approach. 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