In Search of Efficient Walking Robots

Transcription

1 5-5MV-78 In Search of Efficient Walking Robots Brooke Haeisen, Pal Mench, Greg Hdas, James Overholt US Army TARDEC Peter Adamczyk, Greg Hlbert University of Michigan ABSTRACT With the recent conflicts in Afghanistan and Ira, it is increasingly evident that the demands of warfare are changing and the need for innovative mobility systems is growing. In the rogh, nstrctred terrain that the soldiers enconter, they have reverted to sing mles and donkeys to move stealthily and ickly. In light of the growing need for atonomos systems, the Army is looking at the possibility of legged mobility options sch as gasoline powered adrpeds to traverse the off-road terrain. As technology advances, the era of military bipeds may well be in sight. However, crrent bipedal robotic technology is far too inefficient for battlefield se. Mch of this inefficiency stems from actated control of each limb's motion throghot the entire gait cycle. An alternative approach is to exploit the passive pendlar dynamics of legs and legged bodies for energy savings. This paper compares and contrasts flly-actated walking with passive walking. Simlations of passive and asi-passive walking are analyzed to evalate their stability regions and their initial responses on neven terrain fnctions are compared. Figre : Sketch of Fallis' Walking Toy The notion of atonomos mechanical creations originated even earlier with the famos Vacanson s Digesting Dck and other atomata of the 8 th centry (see Figre ). The highlight of this era of mechanical wonders was Von Kempelen s The Trk. Althogh, later proved to be a hoax, this intriging atomaton initiated the fondations for artificial intelligence and emphasized the fascination of a thinking, mechanical hman. INTRODUCTION One of the first walking machines was a toy developed by G.T. Fallis (Figre ), patented in Janary 888. A description from the patent docment provides insight into the mechanics of passive dynamic walking. This invention consists in a toy or figre which may be designed to simlate the hman frame and which is of a combined pendlm and rocker constrction, whereby when placed pon an inclined plane it will be cased by the force of its own gravity to atomatically step ot and walk down said plane... Figre : Theoretical View of Vacanson's Digesting Dck The initial definition of robotics began to take form in the 9 s with the first sage of the word robot in Karl Capek s Rossm s Universal Robots to describe something bilt to perform dll, dangeros, and dirty tasks. The first commercial robot prodced did jst thatit took the position of an assembly-line worker, working heated die-casting machines at General Motors. The robot s name was Unimate, created by George Devol and Joseph Engelberger in 956.

2 Report Docmentation Page Form Approved OMB No Pblic reporting brden for the collection of information is estimated to average hor per response, inclding the time for reviewing instrctions, searching existing data sorces, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this brden estimate or any other aspect of this collection of information, inclding sggestions for redcing this brden, to Washington Headarters Services, Directorate for Information Operations and Reports, 5 Jefferson Davis Highway, Site 4, Arlington VA -43. Respondents shold be aware that notwithstanding any other provision of law, no person shall be sbject to a penalty for failing to comply with a collection of information if it does not display a crrently valid OMB control nmber.. REPORT DATE JAN 5. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE In Search of Efficient Walking Robots 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Haeisen,Brook; Mench,Pal; Hdas,Greg; Overholt,James; Adamczyk,Peter; Hlbert,Greg 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) US Army RDECOM-TARDEC 65 E Mile Rd Warren, MI d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 8. PERFORMING ORGANIZATION REPORT NUMBER SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES). SPONSOR/MONITOR S ACRONYM(S) TACOM/TARDEC. DISTRIBUTION/AVAILABILITY STATEMENT Approved for pblic release, distribtion nlimited. SPONSOR/MONITOR S REPORT NUMBER(S) SUPPLEMENTARY NOTES Presentet at the SAE 5 World Congress, Detroit, MI, The original docment contains color images. 4. ABSTRACT 5. SUBJECT TERMS 6. SECURITY CLASSIFICATION OF: 7. LIMITATION OF ABSTRACT SAR a. REPORT nclassified b. ABSTRACT nclassified c. THIS PAGE nclassified 8. NUMBER OF PAGES 6 9a. NAME OF RESPONSIBLE PERSON Standard Form 98 (Rev. 8-98) Prescribed by ANSI Std Z39-8

3 sheer that, as one soldier pt it, it took me a week to ease the death grip on my horse. One of his conclsions was that It shows that a revoltion in military affairs is abot more than bilding new high tech weapons it is also abot new ways of thinking and new ways of fighting. Robotics is one of those new ways and is taking shape with the deployment of several tele-operated systems sch as the PackBot. Figre 3: Unimate Robot Unimate was operated by a series of programmable motors and actators to control its movements. It falls into the category of robots known as set-point controlled, whose main goal is to follow a prescribed path with minimal error throgh continos actation. The majority of robotics has been focsed in this area with sch stars as Honda s Asimo and Sony s Qrio shown below. Crrently, the Army is working with several companies to explore the possibility of sing walking robots for military se. One prototype ses a bipedal gait to carry a generator for dismonted troops. It is this type of robot that motivates or discssion: How can we improve the mobility and fel efficiency of a walking robot? Figre 4: Honda's ASIMO and Sony's Qrio Biped Robots Albeit the idea of passive walking has been arond for a while, Tad McGeer introdced the theory and renewed interest in the topic, creating a new avene of robotics research based on dynamics. Using simplistic models or rimless wheels and doble inverted pendlms, McGeer was able to mimic hman gaiting. One might wonder why look at walking robots when wheels are an efficient and fast way to locomote from here to there. Wheels are better sited for on-road applications, bt legged robotics has an advantage in the off-road arena becase of its small footprint and low grond pressre. De to the recent conflicts in the Middle East and technological advances, military interest in robotics for off-road applications has heightened. In a Foreign Affairs article by Donald Rmsfeld in, he describes the new war zone: [The troops] sported beards and traditional scarves and rode horses trained to rn into machine gn fire. They sed pack mles to transport eipment across some of the roghest terrain in the world, riding at night, in darkness, near minefields and along narrow montain trails with drops so Figre 5: Concept Drawing of Prototype Robotic Mle One of the possibilities is to se passive dynamics. Some of the advantages of a passive dynamic legged machine are that it reires no energy on a sloped srface compared to a set-point controlled robot. Looking at a asi-passive walker to accommodate positive and level terrain negotiation reires a smaller power spply to provide the necessary actation to overcome gravity and the robots own inertia becase of the tilization of the natral dynamics of pendlar motion. Each movement of the set-point controlled robot is articlated with a host of motors and actators that controls every movement and reires more power becase there are no nderlying dynamics to provide movement dring a step. The passive walker is inherently more robst to variations in the srrondings, sch as pertrbations in the grond, as long as it is given some time to adjst. In example, imagine that a person is walking and stbs their toe on a raised piece of sidewalk. Depending on the speed of the person, they will typically be able to catch themselves before falling. If the changes are too drastic then there cold be problems (imagine the same person is rnning at top speed and not paying attention). The passive walker can also handle larger variations in payloads. If a set-point controlled robot wants to increase its payload, the motors need to be scaled accordingly while the passive walker can add weight with little change in the power reirements.

4 The small motors and actators needed for the asipassive walker, contribte less noise and a lower heat signatre than the set-point controlled robot with its host of motors and actators. Both noise and heat are important considerations for stealth applications in the military. Althogh there are many advantages to passive walkers, there are also disadvantages. Walking machines have been arond since the late 8 s bt passive dynamic walking has not had the same amont of research resorces devoted to it like set-point controlled robots. With companies like Honda, Toyota, and Sony investing in set-point control, the technology in that area is mch more advanced. Another isse is the variety of contact problems possible ranging from toe stbbing, foot scffing, tripping, or all ot collapse. It is difficlt to recover from these withot the actation/motors of setpoint controlled robots. The passive walker is also very sensitive to initial conditions. Withot a stable gait, the passive walker is highly ssceptible to distrbances. Overall, sensor technology is lacking for both passive and set-point controlled walkers. Sensors are necessary to gage the terrain and srronding environment to provide feedback to the robot (think of a person s eyes, ears, toch, taste, and smell senses). ANALYSIS To gain insight into how a passive dynamic walker and a passive dynamic robot following a prescribed path compare to each other, a simlation was created to se the recorded swing leg position,, to provide a tore inpt to the asi-passive walking model. Figre 3 shows a brief schematic of the simlation. otpt Figre 6: Diagram of Problem Setp inpt tore inpt A simple controller was implemented to create a tore to drive the angle to match the prescribed of a completely passive walker in its stable gait. The tore was introdced at the hip as an external inpt to the system. A crved grond with an average eal to gamma was introdced to test the walkers ability to handle a pertrbation sing the same initial conditions for the sloped grond. For extended simlations, a simple sloped grond contines the crved grond at half of the original average slope, γ. Figre 7: Passive Walker Diagram The basic eations of motion for a simplified passive dynamic walker are presented below (). They are based on a doble inverted pendlm system with β representing the ratio of the mass at the foot to the mass at the hip. The model sed for the simlations is a more complicated walker with inertial properties for the hip mass and leg bt the assmptions of a frictionless pin at the hip and rigid legs are still considered. + 3β ( cos( β cos( ) )) β ( cos( β )) && + && β sin( )(( & & ) & ( & & ) + β& sin( ) ( βg / l)[sin( γ ) sin( γ ) g / l sin( γ ) = ( βg / l) sin( γ ) τ hip τ hip The momentm eations based on the simplified eations of motion are shown in (). + 3 = cos θ cos θ A list of the variables sed in the simlation and their vales are presented in the table below. These vales represent an average person s anthropometric measrements, after normalizing by leg length and mass, to non-dimensionalize the model. () ()

5 Variable L = Gamma =.6 Il =.7 C =.645 M =.6 R = Mp =.68 Ip =. G = Meaning Leg length Grond slope Inertia of the leg Distance from foot to leg COM Mass of the foot Radis of the foot Mass of the pelvis Inertia of the pelvis Gravity Table : Walking Simlation Variables The code sed for the simlations was adapted from passive dynamic walker code originally developed by Professor Arthr Ko (University of Michigan). The program integrates the differential eations of motion, stops the simlation when the swing leg connects with the grond (ignoring the first swing leg interaction with the srface when the walker is near vertical- foot scffing), and acconts for momentm loss when the foot impacts grond. Figre 8 shows the basic flow of the program. Variable Stable Vale.76 radians -.76 radians -.49 radians/sec -.97 radians/sec Table : Stability Vales for γ =.6 Another addition was a tore at the hip in the eations of motion. To ensre that the actated walker follows the recorded state vector of the passive walker accrately, a simple proportional-derivative controller was created. CONTROLLER DESIGN The controller design began with a linearized model of the eations of motion. The linearization was done sing the standard Lyapnov method. The eations of motion are set p in the form of the robot eation (3) and then solved for the accelerations (4). M θ & + V ( θ, & θ ) + G( θ ) = τ & (3) & θ = M { τ V ( θ, & θ ) G( θ )} (4) The first step is to transform the eations into state space form. The state variables involved are (angle of the swing leg), (angle of the stance leg), (velocity of the swing leg), and (velocity of the stance leg). The conversion to state space was done throgh the change of variables below. Figre 8: Passive Walker Program Flow One addition is a new event fnction that compares the global y position of the foot with the global y position of the grond and stops the integration when the foot position is less than or eal to the grond at the same x position, ignoring foot scffing. A stable fixed point was also necessary. To find the stable fixed point, the simlation ran ntil the walker settled into its stable gait. A stable gait is one in which the walker will retrn to its periodic motion after a slight pertrbation. Stability is evalated throgh the Floet mltipliers (discrete cycleto-cycle measrements of amplification or attenation of pertrbations) of the partial derivative of the retrn vales (the initial vales for the next step) from the state variables of one step. An example of the state variables for a stable fixed point on a slope of.6 is provided in the table below. 3 4 Once the eations are converted to state space, set the state derivatives eal to zero. After setting the state derivatives and inpt (tore at the hip) eal to zero, the eations are solved for x and x, the eilibrim point. Several different soltions came ot of the eations becase of the sine and cosine relationships. The soltion that is the closest to the typical operating point is chosen as the eilibrim point. The soltions correspond to the following positions in the figre below. Soltion b (γ, -π + γ) is the eilibrim point for the system. (5)

6 Figre 9: Eilibrim Positions of Doble Pendlm The Jacobian of the state space is evalated at the eilibrim point to find the state space matrices A and B. The C matrix is created to track the variable of concern, which, in this case, is the swing leg angle (x ). The sbseent state space matrices were analyzed in MATLAB to create a simplified controller. The final controller is a proportional-derivative controller and its transfer fnction is provided in (6). tf = 6.8s + RESULTS The difference between the original recorded state variable of and the tore driven model over one step is shown in Figre. The controller does a fair job of tracking the original path as the error is on the order of magnitde of E-4. Error (radians) x (6) the crves in Figre, with markers representing the fixed point vales. The variable was chosen for this stdy becase and are symmetric pon impact. There were for sets of recorded angles (γ =.,.6,., and.3) from the passive walker sed as references to drive the tore-driven walker. Generally, as the asi-passive walker is referenced to steeper slopes, its range of application slopes increases. It mst be noted that this is a limited data set and as the slope is increased the robstness will decrease at some point. More tests need to be condcted to find the point at which the range decreases. Another interesting reslt to note is after γ =.4 for the passive walker, a stable period gait develops. Mlti-periodic gait fixed points were averaged for the graphical representation. Smaller increments of slope increases need to be evalated to find the stability limit of the passive walker. Adding the tore and the simple proportional derivative controller extends the range of the passive walker to γ =.75 on the coarse grain of the stdy whereas the passive walker was nstable beyond γ =.5. (radians) passive gamma (radians) Figre : of Fixed Points Parametric Stdy on Sloped Grond To nderstand how a change in the grond fnction affects the two walkers, the grop introdced a sine wave into the slope. The idea was to keep the crve s average the same as the slope. From initial observations, the grond cold change local slope as long as the change was small enogh sch that the passive walker cold adjst within a cople of steps. A simple fnction was chosen for testing with a slight slope (7). Comparing the two, the asi-passive walker did not have as mch variation in its step length. y =.(cos( x ) tan( γ ) x) (7) Time v/(g*l)^(/) Figre : Error in For One Step, γ =.6 Initially, the models were rn with varios sloped srfaces to evalate their stability. The tests prodced

7 Y Foot Position StepLength Grond Tore Passive Step Nmber X Foot Position Figre : Foot Placement and Steplength for Steps on Crved Grond, γ =.6 The addition of the feedback controller and tore smoothes the walker as it traverses the crved slope. The tore history for the asi-passive walker is provided in figre 3. The tore was limited to m foot g l. Realistically, the tore will not be as discontinos. The figre provides an idea of the magnitde of the tores and their freency (histogram in lower left corner). The tores are centered arond zero, so the controller is making only minor adjstments over the dration of the step. Tore (N*m)/(mass * g * l) Nmber of Iterations Figre 3: Tore History for Steps on Crved Grond, γ =.6 FUTURE WORK As noted in the paper, these are preliminary reslts. The grop is interested in performing a set of parametric stdies over a larger range with finer resoltion, addressing the stability conditions and pertrbed grond amplitdes. Other isses to address are the realism of the tore inpt into the system. Some smoothing shold be employed to provide a more continos tore. Many of the fixed points were fond experimentally throgh increasing the nmber of steps ntil a discernible pattern was observed. Frther work needs to be done to improve the search method for these fixed points. Other research topics inclde sing the tore for a portion of the step and allowing the pendlar dynamics of the walker to do the rest. CONCLUSIONS This stdy shows some promising reslts throgh the se of a simple proportional-derivative controller to create a robot driven from recorded state variables. Employing feedback in a system typically enhances the performance and makes it less ssceptible to distrbances. This is evidenced in the increased range of the asi-passive walker to γ =.75 in the simple slope case. In the crved slope experiment, the step length is more niform for the asi-passive robot than in the prely passive case. Comparing the animations of the two models shows the asi-passive walker powering over the slope. It is also worth noting that the asi-passive walker simlation takes at least one hndred times longer to rn. Althogh the tored walker is more robst, there are still many disadvantages to consider. ACKNOWLEDGEMENTS Many thanks are extended to Professor Arthr Ko at the University of Michigan for se of his passive dynamic code in this exercise. REFERENCES. Garcia, Mariano, et. al. The Simplest Walking Model: Stability, Complexity, and Scaling. ASME Jornal of Biomechanical Engineering, Feb Ko, Arthr. Class notes, Mechanics of Hman Movement ME 646, Winter 4. University of Michigan. 3. Ko, Arthr. Dynamics Workbench: Software to Atomatically Generate Eations of Motion, Ko, Arthr. Energetics of Actively Powered Locomotion Using the Simplest Walking Model. Jornal of Biomechanical Engineering, Feb.. 5. McGeer, Tad. Passive Dynamic Walking. The International Jornal of Robotics Research, Apr. 99.