IROS2019国际学术会议论文集 1446

Toward a Bipedal Robot with Variable Gait Styles Sagittal Forces Analysis in a Planar Simulation and a Prototype Ball Tray Mechanism U Huzaifa1 C Fuller2 J Schultz2and A LaViers1 Abstract Variable walking styles in bipedal robots may be used to communicate information about purpose and or personality to human viewers and may also help accommodate features of the environment This paper presents variable gait in a simulation and results from a hardware prototype for gravity driven rolling ball mechanism in a previously proposed bipedal design First optimal control inputs that produce a range of variable feasible gaits is generated on a simplifi ed under actuated planar model Then a tray like mechanism that provides a curved path for a ball to roll on is presented This mechanism is designed to replicate a notion of pelvic shift described in Bartenieff Fundamentals with movement of the ball which is shaped by the tray creating a shift of weight Analysis of two gait styles and two tray designs shows comparable ranges of forces in the direction of travel between the simulated planar model and the hardware mechanism This work is an important fi rst step in generating feasible stable and variable bipedal gaits using this hardware design I INTRODUCTION Humans bipedal locomotion may change based on the internal state or intent of a mover providing an important communication channel between moving agents and their human counterparts For example in evacuating a building a security offi cer will exhibit fi rm directed and steady movement encouraging building occupants to leave in a calm and orderly manner however if signalling the location of a building survivor to a rescue crew the offi cer will use urgent animated and rapid movements Thus gait style communicates features of purpose and personality to human viewers Recreating this behavior in an artifi cial system requires veins of knowledge such as dance and somatics which study and refi ne the creation of varied expression through movement Bipedal robots possess the ability to traverse complex terrain as well as environments built for humans Mechanical bipedal walkers can walk downhill passively 1 2 In actively controlled bipedal robots two classes exist statically stable and dynamically stable robots 3 Robots using a stat ically stable walking strategy include ASIMO 4 ATLAS 5 and NAO 6 Dynamically stable robots on the other hand effi ciently use the dynamics of the robot and inject control input minimally to achieve stable walking movement This in turn leads to energy effi cient walking structures e g Cornell Effi cient Biped 7 that covered a record distance on 1 U Huzaifa and A LaViers are with Department of Mechanical Science and Engineering University of Illinois at Urbana Champaign IL 61801 USA email mhuzaif2 alaviers illinois edu 2 C Fuller and J Schultz are with the Department of Mechanical Engineering University of Tulsa Tulsa OK 74104 USA email caleb fuller joshua schultz utulsa edu corresponding author mhuzaif2 illinois edu a single battery charge A number of robots 8 9 10 in this category use hybrid zero dynamics to make the robot follow a limit cycle behavior There has been considerable work done in developing variations in the gaits for bipedal walkers as well This includes 11 where animations of expressive characters are ported to hardware via trajectory optimization that ensures the hardware satisfi es the Zero Moment Point condition for stability 12 In 13 a gait library is precomputed and employed in run time on the robot for different scenarios In another work 14 gait primitives in terms of stable limit cycles have been defi ned and their composition is studied to achieve navigation through a cluttered environment In computer animation research different bipedal ani mated characters have been studied using similar physics based control schemes 15 16 Other related examples include 17 where different bipedal locomotion modalities and transitions between them were investigated In 18 under variations in an observed walking behavior various stable walking gaits were generated In an attempt to generate different styles of walking a catwalk was investigated on an HRP 2 robot 19 In 20 high level motion primitives were identifi ed and used to defi ne different bipedal walking styles This paper along with prior work 21 22 23 in vestigates an interesting misalignment between the gener ation of bipedal human like gait in robotic platforms and in movement training for humans and how they might be integrated with one another Most bipedal walking robots achieve forward progress by using large actuators located distally and proximally to the center of gravity of humanoid platforms mimicking the anatomical joints in the human legs and hips respectively which experience large deformations during walking In contrast human training emphasizes control via the articulation of the spine and pelvis 24 Bipedal robots that have investigated using an articulated torso for weight shift include 25 with three mobile masses located in its pelvis having 4 DOFs translations along X axis Y axis Z axis and rotation about Z axis In a planar bipedal robot a static inclined torso was shown to increase walking speed for a robot with passive ankle joints 26 Actuation of the torso was also considered in order to laterally stabilize a robot 27 In 28 a humanoid robot with torso made of a Stewart platform and capable of rotations in 3D was simulated Study of related works in bio mechanics 29 30 highlights the importance of the pelvic muscles in human walking and other physical activities This paper presents 1 variable gait generation using an optimization framework and a centrally located actuator and 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE2266 2 a hardware mechanism that meets an initial benchmark for producing forces in the sagittal dimension to embody these gaits In this hardware implementation carefully timed tray tilt can induce major displacement of the center of mass of the robot by shifting the location of a relatively heavy mass as it navigates the tray s channel Varying the shape of this tray changes the force profi le which according to simulation results also changes the style of gait The rest of the paper has the following structure Section II reviews the high level embodied ideas about locomotion that inspire this work Section III discusses the planar biped model and variable gait generation as a feasibility problem solved using trajectory optimization In Section IV we present the hardware design for the tray structure emulating the human core particularly the net effect of the pelvic girdle shown in Fig 1b In Section V the experimental force profi le from the hardware platform is analyzed and compared with force in the planar model simulations Section VI concludes the work and proposes future directions II INSPIRATIONFORVARIABLEWALKINGSTRATEGIES FROMEMBODIEDMOVEMENTANALYSIS Bartenieff Fundamentals is an example of a somatic or body based analysis of movement 24 Such somatic practices as they are called present movement from an internal embodied point of view In this way movement is understood in combination with articulated strategies and internally perceived body connections to one s own body and the bodies of others Within Bartenieff Fundamentals a set of six conceptual exercises named the Basic Six create a link between bodily movement and the mover s intention These exercises have shown to be useful in re patterning human movement for people with motor disabilities as well as professional dancers Three of the Basic Six shown in Fig 1a describe locomo tion Thigh Lift Forward Pelvic Shift and Lateral Pelvic Shift Thus according to this framework the to and fro movement of the pelvis along the path of travel is a major contributor to locomotion The lateral movement of the pelvis on the other hand is helpful in making room for the swing leg to pass through Moreover with variation in these elements a range of walking styles can be obtained This insight about the role of the pelvis helps identify the pivotal role played by the pelvis or core in the human body and forms the basis for our hardware design In 21 a robot design was proposed shown in Fig 1b to recreate the action of the human pelvis in walking This design has a tray like structure on top of the two legs in a biped robot making an analogy to the motion of the human pelvis The tray structure has a curved path in which a relatively heavy ball of mass can roll The tray can be actively tipped about the pitch Y in Fig 1b axis and as a result the ball can roll through the curved channel producing force along the path of travel and perpendicular to it The design was created after extensive embodied exploration of Bartenieff Fundamentals Our goal was to physically approximate the spatial path of a weighty pelvis as opposed to replicating the relative a b c Fig 1 The analogy between a human strategies for walk ing b envisioned robot design presented in 21 and c the planar model utilized here The pelvis is emulated by a sliding mechanism moving the mass Mtforward and backward by displacement dt Variable gait Parameters TL and PS allow multiple gait styles to be generated motions of distal and proximal joints like ankles knees and hips as other human inspired walking techniques have used Thus a top down design effort to create a similar oblique weight shift on a robotic platform led to the development of a ball tray mechanism as shown in Fig 1b in 21 In this paper a prototype that fulfi lls key benchmarks for hardware implementation of this design will be presented III VARIABLEGAITGENERATION INPLANARBIPED MODELWITHCORE LOCATEDACTUATION Prior work with a planar compass walker has shown that it is possible to generate and classify a range of different gait styles using optimization 23 This work leveraged a joint investigation of the movement vocabulary provided in the English language and methods of observation provided by Certifi ed Movement Analysts user studies then validated the stylistic labels applied to each gait In this section similar variations will be shown for the core located actuator design that can be similarly labeled through iterative design A planar model of a bipedal robot in Fig 1c is used to develop periodic variable gaits in simulation To model the action of the core especially pelvic motions in humans the planar model has an actuated prismatic joint moving a mass forward and backward The orientation of this mechanism is 2267 fi xed along the X axis in Fig 1b A hybrid model is used to represent the walking dynamics In the swing phase the biped acts as a three link planar robot fi xed at the stance leg foot The generalized coordinates qs qst qsw dt T represent the absolute angle of the swing leg qsw the absolute angle of the stance leg qst and the displacement dt of the core mass Mtfrom the hip The corresponding state vector is xs qst qsw dt qst qsw dt T The swing phase is active until the swing leg impacts the ground Fig 2 The Euler Lagrange equation for this phase is the same as in 22 except that here we are using an under actuated model where only the swing leg along with the core mass is actuated The mass centripetal Coriolis and gravity matrices and non conservative terms that describe the swing phase dynamics are given in Appendix A At impact the joint positions and joint velocities are updated Consequently the two leg joint angles simply exchange their roles while the core located mass displacement from the hip remains the same The post impact joint velocities are determined by assuming that the swing leg instantly stops moving parallel no slip and perpendicular to the ground no rebound Fig 2 Planar biped model for forward pelvic shift Gait parameters TL and PS specify the step length and the desired path for dt respectively The biped model stays in the swing phase until the swing leg impacts the ground To fi nd periodic feasible and variable gaits for this model a feasibility problem is formulated by establish ing variable constraints in an optimization with a constant objective function as implemented in 31 Among the constraints there are path constraints which are satisfi ed throughout the walking step and boundary constraints which have to be satisfi ed at the two ends of a walking step Gait parameters TL inspired from Thigh Lift and PS inspired from Forward Pelvic Shift are defi ned as well to embed the ideas of step length and variable waveforms of dtin the optimization constraints as also indicated in Fig 2 The path constraints include the dynamics of the biped model that the normal ground reaction force on the stance foot Fst N t must be positive that the ratio of the ground reaction forces must lie in the friction cone satisfying F st N t Fst T t where is the coeffi cient of friction for the walking surface and the desired trajectory for dtbe defi ned by the gait parameter PS Fig 3 The boundary constraints include the step length constraint defi ned by the gait parameter TL and a periodicity constraint at the end of the walking step Thus using these constraints the feasibility problem for mulation for a periodic gait over a walking step is as follows min u t J u t s t xs D 1 s Cs qs Gs s Fst N 0 Fst T Fst N r sin qst tf sin qsw tf TL r cos qst tf cos qsw tf 0 dt ddes t PS 2 0 xs 0 xs tf xsmin xs xsmax umin u umax t 0 tf 1 The objective function J is chosen to be a constant 100 for all choices of PS shown in Fig 3 Thus this optimization with a constant objective function forms a feasibility prob lem we search for a feasible solution satisfying the given constraints adjusting TL and PS to fi nd a new style of gait The biped model parameters and the range of values for state and input vectors are given in Table I SymbolName Value or Range of Values lower limit upper limit u1Swing Leg Torque 100 100 Nm u2Force on Core Mass 100 100 N qst qsw TLeg Joint Angles 2 2 2 2 T dtDisplacement of Core 2 2 m qst qsw TJoint Angle Velocities 5 5 5 5 Trad s dtVelocity of Core 5 5 m s MtCore mass1 089 kg mMass of each leg0 544 kg rLength of leg1 m TABLE I Range of input and state vectors and values of model parameters used in the optimization problem Eq 1 for fi nding gaits of the given biped model The solution to this problem an input trajectory and initial conditions giving a new gait style has been investigated for TL 0 1 0 2 0 3 0 4 and 0 5 and fi ve pre defi ned options of PS given in Fig 3 which are currently chosen in an ad hoc manner The nonlinear optimization problem is then solved using IPOPT 32 and the function approximation is performed using the Legendre polynomials The optimization toolbox used for this purpose is GPOPS II 33 and is run in a minute or less on a laptop computer running a 2 2 GHz Core i7 processor The code is written in MATLAB using the toolbox in 34 which leverages direct collocation 35 IV HARDWAREIMPLEMENTATION OFCENTER OFMASS SHIFT BALL TRAYMECHANISM Since the gait of the planar model can be deliberately modulated by imposing motion of the mass of the core at key junctures in the gait we need a physical mechanism that can sit atop a robotic walker imposing forces in a cyclic manner A light tray with a heavy ball actuated by a DC motor is proposed as an embodiment of the solution in 21 2268 Fig 3 Snapshots of a few gaits generated by varying the gait parameters in Fig 1c and solving Eq 1 Gait parameter TL corresponds to the step length and PS corresponds to the waveform of dtover the duration of a step By tilting the tray the ball will roll in the channel producing motions analogous to both the thigh lift and the pelvic shift As the ball traverses the curvilinear path the reaction forces that maintain the path of the ball will be transmitted to the walker modulating the gait Furthermore the collision with the ends of the tray impose impulsive forces which could be transmitted to the walker either reinforcing or arresting the current step Finally it is envisioned that the dynamics of the step and the collisions of heel strike could back drive the ball to a greater or lesser degree by actively varying the tray tilt by a control system By changing the shape of the tray and tray tilt the gait can be modifi ed The change of shape of the tray is analogous to the parameter PS from the feasibility problem defi ned in Section III and the tray tilt is analogous to the parameter TL from the feasibility problem We examine the reaction forces produced by the ball tray system and show that it is capable of producing force profi les of comparable timing and range as in the simulated model of Section III In the simulation of the planar biped model a heavy mass moves back and forth at velocities on the order of 2x the stride frequency with the mass heavy enough to affect the dynamics This would require a large heavy linear actuator Tilting a tray however and allowing the ball to roll can be accomplished with an actuator of comparatively modest size and the impact at the ends of the tray and navigating tight curves can still produce appreciable reaction forces The ball tray dynamics are then functions of the shape of the tray as well as the ball rotation position in the tray and tray angle A prototype ball tray system is placed on top of an experimental frame for characterization A Tray Fabrication Method The tray is constructed from carbon fi ber composite formed around a foam negative mold which is itself con structed from a Fused Filament 3 D printed positive This allows physical rails to be molded into the carbon fi ber profi le minimizing rolling friction This process allows trays to be constructed quickly with many shapes The high strength to weight ratio of the carbon fi ber composite renders the tray light compared to the ball improving the analogy to the planar model Two trays were tested both V shaped with a 12 7cm radius circular bend