Force Sensing for Walking Robots

Transcription

1 Force Sensing for Walking Robots U. Schmucker, A. Schneier, V. Rusin2, Y. avgoroniy2 Fraunhofer Institute for Factory Automation an Operation, Santorstr.22, 3906 Mageburg, 2 University of Mageburg, ostfach 420, Universitätsplatz 2, 3906 Mageburg, Germany schmucker@iff.fraunhofer.e, schnei@iff.fraunhofer.e, rusin@iff.fraunhofer.e, zavgo@ieee.org Abstract In this paper it is shown that by using force information, it becomes possible to solve a large number of tasks. Force control is neee to increase the aaptability of the vehicle to irregular terrain an to istribute the foot forces uring locomotion over rigi an soft soil. Spatial movements of a legge robot s boy are use for service tasks with constraine motion. The algorithms base on the information about the vectors of main force acting on the boy have been evelope. Eperimental results are presente. Ine Terms force control, force istribution, legge locomotion, service operations I. INTRODUCTION T HIS paper we want to attract attention of researchers an esigners of walking robots to the problem of force sensing for similar vehicles. The use of force information allows such systems to achieve the new mechanical properties, to increase reliability an functional capabilities of walking robots, an to simplify many control algorithms. It is clear that the force istribution calculation requires that the legs of the robot be equippe with force sensors Fig.) an that force feeback shoul be introuce into the control system. The algorithms for force control are base first of all on the following impeance control laws: active compliance, active accommoation, an hybri position/force control. It is possible to specify the following basic irections of major tasks an researches of motion control of walking robots where it is necessary to use force control. This work was financial supporte from Germany Research Founation DFG. U. Schmucker is with the Fraunhofer Institute for Factory Automation an Operation, Santorstr.22, 3906 Mageburg, Germany corresponing author to provie phone: ; fa: ; schmucker@iff.fraunhofer.e). A. Schneier is with the Fraunhofer Institute for Factory Automation an Operation, Santorstr.22, 3906 Mageburg, Germany schnei@iff.fraunhofer.e). V. Rusin is with the Otto-von-Guericke University of Mageburg, ostfach 420, Universitätsplatz 2, 3906 Mageburg, Germany rusin@iff.fraunhofer.e). Y. avgoroniy is with the Otto-von-Guericke University of Mageburg, ostfach 420, Universitätsplatz 2, 3906 Mageburg, Germany zavgo@ieee.org). A. Local regulation an gait cycles correction of legs This is the organisation of an aaptive step cycle for each leg or stepping over an unknown obstacle by means of touching movements. B. Force motion control of legs in interaction with a support surface One of the central problems of motion control is the force istribution between the legs, an the motion organisation of the robot in margins of static stability. The control of support reactions is necessary uring the movements on rough terrain an to increase groun passability. A multi-legge walking vehicle is a statically ineterminate mechanical system with respect to foot forces acting on its legs. This feature allows algorithms for the istribution of support reactions for rigi an compliant surfaces [,2], to consoliate the groun [2] an to carry out movement an manoeuvring of a robot. In locomotion over comple terrain, the necessity may arise to control the horizontal force components so that contact forces are within friction cones [, 4, 5]. Active istribution of support Fig.. 3-component reactions makes it possible to reuce force sensor loas on the vehicle structure an the energy consumption of leg rives. The possibility of force istribution control in a walking vehicle has been iscusse for more than 25 years. There are a number of approaches to the istribution problem base on ifferent criteria, e.g., [,4,6]. At present it is clear that in orer to achieve force istribution by any metho requires that the vehicle legs shoul be equippe with force sensors an that force feeback shoul be introuce into the control circuit. Such an approach is for a long time wiely use in manipulator systems. C. Force control of robot's boy manoeuvring The capabilities of walking robots are not merely limite to the transportation of ifferent objects or technological equipment. They can be use as the multi-purpose chassis for performance of various technological or service operations.

2 2 Many of such operations assembly, hanling, rilling tasks, repair tasks, machining) shoul be carrie out by control of contact forces ue to interaction with objects. These tasks may be also treate as constraine motion problems. D. Force control of locomotion in problems of climbing, large obstacles overcoming an etc One of the basic avantages of walking robots in comparison with wheel an caterpillar machines is the opportunity of moving over a ifficult terrain region), of overcoming larger obstacles by climbing over them, movement over "hummocks", stones, etc. These works substantially are at a stage of computer moelling [7,8], the eample of technical realization of movement in a pipe is escribe in [5]. E. roblems of movement stability, oscillation amping roblems of movement stability an oscillation amping, that can occur in the boy an legs of the robot owing to interference of leg's movements through a groun contact area or because of interaction of tool installe on a boy with an environment. However, when there is feeback with respect to the support reactions, the control signals in each leg epen on the boy motion of the robot, an thus on the motions of the other legs. A source of oscillations in system also can be the coefficient of gains, time elay in the force feeback, stiffness of force sensors, an mass of boy [2, 9, 0]. The results of this paper are base on longstaning eperience at the Fraunhofer Institute for Factory Operation an Automation IFF) in the evelopment of si-legge walking robot "Katharina" weight about 25 kg) with heagonal boy Fig. 2), which was equippe an aitional manipulator evice with two egrees of freeom []. Some results have been obtaine earlier by evelopment of prototype "Katharina" - si-legge walking robot "Masha"weight about 22 kg) with rectan gular boy [2]. Both vehicles have si legs with three powere egrees of freeom each an are equippe with threecomponent force sensors mounte in the shanks Fig. 2). The manipulator has threecomponent force sensor as well. Fig.2. Si-legge robot "Katharina" uring rilling operation II. USE OF FORCE INFORMATION IN CONTROL OF LEGGED ROBOTS A. Main approaches an principles of force control Manipulator control approaches using force information can be subivie into major groups. The first group of approaches uses logic branching of control when the measure force satisfies certain conitions. The secon group introuces continuous force feeback on the approaches as an eplicit force control or active force feeback metho. The force feeback methos which are alreay use or can be applie for control motion of walking robots are iscusse in many works, e.g., [9, 2-6] an other papers. Stiffness control is the simplest metho of linear force feeback: u = c F F ), where u is a voltage applie to the rive, F is an applie force, F is a reference force, an c is a compliant coefficient. If the force sensor is very har stick, then this feeback has a very high gain. For such feeback, the naturally present amping in the system can be insufficient resulting in a highly oscillatory system. To increase the amping, a velocity feeback shoul be introuce in the system. Active or artificial compliance metho has been evelope for use of robotic systems an also si-legge robots. The most easy law of this metho has the form: = c F F ), ) where is a co-orinate of en-effector, is a reference coorinate an F, F are an applie an reference, accoringly, c is a esire compliance. In [7] applie for si-legge OSU heapo force control in the law form: z& = z& g z z) g F ), 2) F F where z an z& are the actual vertical leg position an velocity, z an z& are esire vertical position an velocity, g, g F are gain. In [2,2] use somewhat other law so that an eternal force acting on the legs of legge robot "Masha" will lea to a isplacement of en-effector. In Fig. 3 are shown interaction of the positional an force parts the control system for leg of walking robots "Katharina". Suppose that the servosystems track the commane co-orinates if the leg tips to a high egree of accuracy. Write the raius vector r of the i -leg in the Fig. 4. Downwar-motion of boy boy-fie co-orinate system as: r = r δr, where r is the commane position of leg motion algorithm, δ r is force correction. Because of force feeback, the positional servo-system receives the leg position, which iffers from r as: δ r = Λ N N ), 3)

3 3 where matri, Λ is the symmetric positive efinite feeback gain N v an N are actual an commane force vectors, accoringly. If the force acting on the leg iffers from the commane value, it causes an aitional leg isplacement proportional to the ifference. Such behaviour of the system is similar to that of an elastic spring with compliance Λ. Compliance can be controlle by varying the elements of the matri Λ. Active accommoation or generalize amping control. The esire en-effector behaviour is also often specifie as a amper behaviour of the form as & v = g F F ), where & is an en-effector velocity, v is a reference velocity, F is a reference force, an g is a amping factor. By that eternal applie constant force acting on the en-effector will lea to a steay state motion with the velocity proportional to the force. The theoretical analysis of this metho an eperiments are escribe an stuie in many works, e.g., [9, 4, 6], in book [8]. It is base on the information about the force/torque vectors use for planarparallel isplacements an angle orientation of boy with respect to the support legs. If the commane vectors of linear an angular boy velocities V = G F F ) ; ω G M M ) ) epen f p Fig.5. Upwar-motion of boy = ϖ on the force an torque, than the vehicle boy will move in accorance with the "accommoation" or "generalise amping" concept. In Figures 4-5 are shown eperiments with robot "Katharina". The eternal force has been impose with the ynamometer connecte with the boy. It can be seen that the isplacement of the boy became responsive to the eternal reaction. Impeance control. In a more general way, the relation between the eternal force an the manipulator motion can be specifie as a esire impeance of the manipulator, e.g., [9, 5, 20]. The impeance can be efine as a transfer function between the eternal force acting on the manipulator an its isplacement. The specifie impeance can be achieve by ifferent means - by using implicit or eplicit force control. Hybri position/force control [3, 4]. Some egrees of freeom of the en-effector are position controlle an the other force controlle. This metho is base on the concept of a selection matri, which is a iagonal 66 matri with zeros an ones on the iagonal. In the theory an practice of force control of robotic systems are also known more comple laws of control which review can be foun in many publications, an books, e.g., [6,8]. B. Force control for step aaptation To move a vehicle over irregular terrain with small roughness, an aaptive step cycle of legs has been evelope for the robot "Masha" Fig.6). It consists of si straight line segments. Any time the force sensor of leg touches the groun within segment 6), the vertical movement is stoppe, an the trajectory of the foot is moifie as shown in Fig. 6 by ashe line, the time of the whole cycle being constant [2,2]. C. Distribution of vertical force components First we shall consier a situation when a force feeback control is absent. In Fig.7 are plotte the vertical force components of support reactions in legs. As the system statically ineterminate with respect to forces acting on the legs on a support can be more than three legs), so support reactions change in a ranom way. It can lea to significant mechanical loaing upon separate legs. The force istribution control essentially improves a locomotion pattern of the robot an increases a stability of robot motion. Force istribution can be etermine by several methos within the framework of statically ineterminacy. Let the walking robot move relatively slowly, an therefore the influence of ynamic factors on force istribution may be neglecte. The commane vertical forces components were compute from the boy orientation relative to the gravity vector, an from the leg configuration. They must satisfy the static equilibrium equations: N, N X, N y Y, 4) = = where is the vehicle weight, Fig..6: Aaptive step cycle Fig.7. Eperimental results of foo forces in locomotion over rigi surface with tripo gait =, y are co-orinates of

4 4 the i -th leg tip, an X, Y are co-orinates of the vehicle center-of-mass [2]. It is clear that if n >3, the solution may be chosen ambiguously. There are ifferent ways of eliminating the ineterminacy. Let us require that the vertical force components shoul satisfy: 2 N ) min 5) This conition has the sense of energy optimisation. The eact conition of energy optimisation is more comple, an it has been consiere in [4, 7]. Fig. 9. Simplifie moel of mass istribution. For the ecision of the equations 6) it is necessary to calculate the co-orinates X,Y) of the vehicle center-of-mass in terms of the legs configuration. The simplifie moel of mass istribution has been mae: the legs with mass point m locate on the leg ens an the boy of mass M B = M 6m, where M is the total mass of the vehicle s. Fig. 9) [2]. The solution for equations 4) may be written in matri form as AN =. The solution of these equations uner conition of 5) is = A, where A N O s = A ) T AA T is the pseuo-inverse of matri A.This solution can be obtaine using Lagrange multiplier [27]. Here I enotes the set of the supporting legs. This scheme for calculating the vertical force components was suggeste by Walron [6], an use in [2]. Fig.8. Eperimental results of vertical components of force istribution surface with tripo gait There are the eperimental results obtaine in the locomotion of multi-legge robot "Masha" over an even rigi surface with the tripo gait. In Fig. 8 are plotte the eperimental results in the control of vertical force istribution in robot locomotion. As can be seen, the vertical force istribution an the stabilisation of the boy motion are tracke with goo precision, an uring the joint support phase one set of legs is loae, another is unloae. Reistribution of loas is smooth, without jumps, as istinct from the situation when forces are not controlle. More etaile results to contain in work [2]. D. Determination of groun mechanical characteristics A eformation of a groun uner supporting legs leas to a moification of a robot motion. Due to vertically sinkage the supporting leg foots in a soft soil it is necessary uring every step to maintain the correct position of the boy relative to the surface by controlling the angular an vertical velocities of the boy. This leas to increase of energy consumption by a movement. A shear eformation of a groun leas to reuce of vehicle velocity in absolute space. The walking vehicle leg provie with foot force an joint angle potentiometer Fig.0. Loa-sinkage relation for the san sensors is the ieal evice for compressive "loa-sinkage" relations an shear groun measure ment. In Fig.0 is shown the eperimental loa-sinkage relation for san soil. The mechanical properties various soils, robot loco motion over soft elastic, consoliating, an consoliating with intermeiate loaing) soil an istribution of force reactions have been eperimentally investigate [2]. E. Constraine motion control The walking machine can be use as an aaptive hanling platform with si egrees of freeom on which the processing equipment for performance of working or service operations can be establishe. Many service an process operations may be consiere as a motion with a mechanical constraint impose on the manipulate objects, e.g., [4, 8]. Similar situations arise by the force control of the legge platforms as the manipulation robots. In [8] is escribe the generalize approach to the synthesis of manipulator system as a superposition of two basic motions - at the normal an at tangent to the contour. A motion of en-effector in the irections normal to the constraint is controlle using the force sensor; a motion along the constraint, i.e., at a tangent to the constraint is uner positional control. Accoringly, the «esire» velocity vector V of a tool or manufacturing equipment is as a sum of two terms V = V V = λ F F ) n Vττ 6) n τ n Here n anτ are the vectors of the outer normal an the tangent with respect to the surface, V τ is the programme value of the tube velocity along the tangent to the surface of

5 5 the object contour velocity), V n is the programme value of the normal component of the contact force to be maintaine, F is the normal force component, λ > 0 is a constant. If n the friction between tool an surface is absent or known then the vectors n an τ can be etermine from force sensor signals. If the constraint is not known eactly, the motion of the boy with the manipulator can be etene to all irections. In this case, the compliance motion of the boy can be implemente with active compliance or amping control. III. FORCE BODY MOTION CONTROL FOR SERVICE OERATIONS A. Force control of motion boy by assembly operation tube-in-hole insertion An assembly task is emonstrate here by insertion of a tube with iameter 0 into a funnel shape hole of an eternal object, whose position is unknown Fig. ). The tube is rigily Forcesensor connecte to the boy Tube &y n 2s of a heapo vehicle v n F 2 by a force sensor. Its s s aial irection is & n parallel to the OX F F F v n p 2s p n ais, which is rigily v t relate to the boy Fig.. Inserting a tube into a hole an its origin in the boy centre. The surface of the eternal object is a funnel-shape hole with a iameter > 0. We use the metho base on the measurement of the reaction force components ue to contact between the tube an the funnel-shape surface, an accoringly move the boy of the robot in such a way as to minimize the reaction forces. The tube moves towars the hole an touches the inner sie of the funnel. During this motion the force components are measure. This approach performs the measurement of the components of the force vector by contacting the tube en with the funnel-shape surface, maintaining a constant contact force equal to the programme value, an moving the robot s boy with the tube in the irection of the hole. For the motion of boy control have been two moes of force control investigate - with inepenent an with superposition of motions. The accommoation matri G is set iagonally. Its elements are ajuste so that they are f Fig.2. Superposition of initial an finite states of the robot big for movements perpenicular to the hole an small for movements along the tube ais. B. Algorithm superposition of boy motions In orer avoi losing contact between the tube an the funnel surface we use the control law as a superposition of two basic motions motion a normal an tangential to the funnel-shape surface. We also ae the constraint that the motion along a normal shoul maintain a constant force contact between the tube an funnel surface. Accoringly, the programme value of the tube velocity may be represente as the sum of the two components in accoring with eq. 6). In [22] the program of boy velocity isplacement epening on components of an eternal of force/moment vectors is certain. Coefficients V F of the system of equations 6) have τ,, λ been selecte eperimentally an were equal to: V τ = 0,7cm/ s, F = 30N, λ = 0,4cm/ sn. The eperimental results have shown that the contact between the tube an the funnel-shape surface was not lost. In Fig. 2 show two positions initial an finite) of the robot uring the eperiment. C. Force control of motion boy for the rotating a hanle Let us consier a task of rotating a hanle with a ro mounte with a force sensor on the boy. Similar tasks of the rotation of the hanle or the steering of a wheel by means of a manipulator were stuie, e.g., [4, 5, 8]. In eperiments Fig. 3), the force sensor is attache to the en of the manipulator arm fiture on the boy of the legge robot. The other en of the sensor is connecte to the tube that comes in contact with the hanle. In this task, only two boy translation egrees of freeom to control the motion of the hanle are use. To rotate the hanle, it is necessary to move the boy of robot together with the tube) along the circumference. In oing so, each point of the mast shoul move along a curve closely approimating a circle but for all that a position of the circle centre an its raius are a priori unknown. Fig.3. Rotating of hanle Let the constraint is bining bilateral), then it is possible to accept F = 0, an epression 6) will be the form V = gf n vτ 6) n If the friction in the hanle ais an the hanle mass are negligible, then the force eerte on the sensor by the hanle is always in a irection tangent to the raius. By measuring the vector F of this force, we etermine the vector of normal n = F / F, an therefore, the vector of tangentτ.then we can rewrite 6) as follows:

6 6 = 7) V gf vτ It seems that 7) may also use when the force of resistance to the hanle rotation is nonzero, but not too large. The escribe control law were successfully applie in the eperiments. The general view of eperiments is shown in Fig. 3. D. Force control of motion boy by rilling operation For the use of the boy together with a rill as a working evice it is necessary to control the boy movement in such a way that the longituinal ais of the rill is collinear to the normal irection of the parts surface. rocess of rilling consists of some stages: efinitions of a normal to surface an orientation of a boy angle ϕ of the slope working surface) together with rill, an the rilling action. Definition of a normal an rill orientation is carrie out as a result of efinition of co-orinates of a surface in several points of contact between the rill an the object. During orientation of the boy, the inclination-sensor measures the actual tangential eviation θ of the boy. If ϕ is θ ) smaller than the given value the movement of the boy is stoppe. During rilling, the commane vectors V an ω of the boy epen on the force an torque as V = k F F ) an V = ω R, where X F F, F X y sensor, X X X, are force components measure by the force k k, k X, is the feeback gain, R is a constant escribing the istance between the co-orinate frame an rill en, then the vehicle boy will move in a given irection. In Figure 4 the plots of the longituinal Y isplacement ) of a ) of rill an force components rill an force reaction components uring rilling are shown. F Fy Fz,,c Y IV. CONCLUSION A control system base on the interaction force information is aequate to solve the problem of locomotion a legge robot or the boy isplacement along a constraint most applications require this kin of control). The implementation of impeance force control - active compliance, accommoation, hybri position/force control - simplify the series of algorithms an increase the fiel of application of walking robots. Develope evices an force control algorithms can be put in a basis by evelopment of new laboratory moels, an full-scale walking robots, their F Fy Fz t, Fig.4. lots of the longituinal isplacement F, F, F p y z sensors, force systems an algorithms of control. REFERENCES [] Shin.-Min Song an K.J. Walron, Machines that walk: The aaptive suspension vehicle, The MIT ress, 34 p., 989. [2] D. M. Gorinevsky, A.Yu. Schneier, Force control in locomotion of legge vehicle over rigi an soft surfaces, Int. J. Robot. Res. Vol.9, No.2, pp.4-23, 990. [3] R.B. McGhee, Vehicular legge locomotion, In Avances in Automation an Robotics. Greenwich, Conn. Jai ress, Inc., 985. [4] D.E. 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