Motion Planning and Feedback Control forBipedal Robots Riding a Snakeboard

Jonathan Anglingdarma, Ayush Agrawal, Joshua Morey and Koushil Sreenath

Abstract— This paper formulates a methodology to planand control flat-terrain motions of an underactuated bipedalrobot riding a snakeboard, which is a steerable variant of theskateboard. We use tools from non-holonomic motion planningto study snakeboard gaits and develop feedback controlstrategies that enable bipedal robots to produce the desiredgaits while maintaining balance, regulating the magnitude anddirection of the velocity of the snakeboard, achieving sharpturns, and avoiding obstacles.

I. INTRODUCTION

Legged robots are highly versatile machines that exhibita wide variety of locomotion modes like walking, runningand jumping which enable them to traverse over extremelyrough terrain unlike wheeled robots. On flat terrain however,wheeled robots outperform their legged counterparts in both,speed and energy efficiency. This paper attempts to bridgethis performance gap by introducing a faster and efficientalternative to legged locomotion on flat terrain - riding apassive wheeled platform. With this research, we hope tooptimize the ability of legged robots by offering them amedium where they could use a wheeled platform to travelfaster on smooth terrains while also having the option towalk or run in more challenging terrain. In particular, wedevelop control strategies for a high degree-of-freedom andunderactuated bipedal robot, Cassie1 to autonomously ridean unpowered wheeled platform known as the snakeboardas illustrated in Fig. 1.

The snakeboard is composed of a central bar that connectstwo rotating pads where the rider places their feet. Theserotating foot-pads are connected to the axles of the wheelsand allow the rider to independently steer the wheels. Unlikea skateboard, the snakeboard allows the users to propelthemselves by rotating their body and the foot-pads, withoutthe need for placing their feet on the ground. By interactingwith the snakeboard pads through different gait patterns, therider can achieve various motions in the inertial frame.

A. Challenges

Enabling a bipedal robot to safely ride a snakeboardinvolves many challenges. First, snakeboards are highlydynamic platforms that are sensitive to the input forces

This work is supported in part by National Science Foundation GrantCMMI-1944722.

The authors are with Department of Mechanical Engineering, Universityof California at Berkeley jonathan ang@berkeley.edu,ayush.agrawal@berkeley.edu,joshuamorey@berkeley.edu, koushils@berkeley.edu

1Cassie is a bipedal robotic platform developed by Agility Roboticshttps://www.agilityrobotics.com/robots#cassie.

Fig. 1: Cassie Riding a snakeboard along a sinusoidal path.A video of the simulation results can be found here: https://youtu.be/fapcnAvYbko

and thus, being able to balance on them is challenging.Second, Cassie can only control the snakeboard motionwhen the contact between its feet and the board is sustainedand no slip occurs. Therefore motion plans and controldesign should provide these additional guarantees. Third,rapid modulation of torso yaw momentum is a criticalcomponent in snakeboard propulsion. Since Cassie is arm-less, this ability is severely constrained. These limitationsrestrict the range of feasible gaits for riding the snakeboard.Cassie is also a high degree-of-freedom, under-actuated robotmaking the system challenging to control. In addition, ridinga snakeboard also requires achieving multiple tasks suchas oscillating the hip joints, leaning the body forwardsor sideways, and maintaining stable balance. In order toaddress these challenges and successfully execute dynamicflat-terrain motion plans, we propose an operational spacecontroller that allows Cassie to achieve multiple tasks, whilealso maintaining friction constraints between the foot and thesnakeboard pads.

B. Related works

Multi-modal locomotion, and in particular, combiningwheeled and legged locomotion is an active area of research.There is a great variety in the types of systems that are paired,the control methodologies used, and how contact betweenlegs and wheels is enforced. For instance, the authorsin [1] integrated and successfully demonstrated wheeledlocomotion of Cassie with hovershoes and with segways in[2]. The work with ANYmal in [3], is another example ofmulti-modal locomotion which combines the advantages ofboth walking and using wheels at its feet. Ascento [4], is alsoa mobility robot that uses a combination of legs and wheelsto maneuver quickly on flat terrain while also being able

to jump and avoid obstacles. Quattroped [5] is a quadrupedrobot that can transform its legs to wheels which can beutilized for better performance and efficiency for differentground locomotion platforms.

With regards to combining legged locomotion with passivewheeled devices, [6] considers the problem of stabilizing aplanar bipedal robot on a ball. In [7], the authors presentan MPC framework to manipulate a ball using a quadrupedrobot to follow desired trajectories. The work in [8] developsa framework for a 3D humanoid robot to ride a passiveskateboard.

The snakeboard considered in this paper is a dynamicalsystem with non-holonomic constraints and motion planningfor such systems has been extensively studied in prior work,beginning with [9] that considered various sinusoidal gaitsfor the snakeboard joints which was later extended to anoptimal control framework in [10]. The work in [11], [12]formulated the motion planning problem of steering thesnakeboard to a desired goal location by considering variouskinematic trajectories. In [13], the authors propose a gaitgeneration technique to achieve displacement along a givendirection and present an analytical framework in [14] forthe joint configurations to follow desired trajectories in thetask space. In [15], the authors consider the problem oftrajectory planning by considering only the local curvatureof the desired path and in [16] analyze the snakeboard withviscous friction. In [17], the authors analyze human riderson a waveboard, which is another form of a system withnon-holonomic constraints.

C. Primary Contributions

Our work draws motivation primarily from the studiesmade in the non-holonomic motion planning for snakeboards[9] and a force balance control strategy for bipedal robots[18]. In this paper, we modify gaits so that Cassie couldachieve some desired features for trajectory planning andcompute the desired center-of-mass for Cassie to still be ableto maintain its balance while riding on the snakeboard.

Distinct from prior work in [3], [4], [5] which considerthe wheels to be fixed to the legs or [1], [2] whichconsider combining powered wheeled devices with leggedrobots, we present a trajectory planning and optimization-based feedback controller for a bipedal robot, Cassie toride a passive wheeled platform, the snakeboard. Throughour proposed framework, the combined Cassie-snakeboardsystem is able to follow desired trajectories in the task-space,achieve sharp turns and avoid obstacles, while maintainingbalance and friction constraints.

D. Organization

The rest of the paper is organized as follows. SectionII describes the dynamical model of Cassie integrated withthe snakeboard. Section III discusses different approachesfor generating various gaits to propel the snakeboard alongdifferent desired trajectories. Section IV presents a balancecontrol strategy for Cassie to be able to achieve the differentgaits and regulate the center-of-mass and angular velocities

TABLE I: Physical parameters of the snakeboard.

Symbol Descriptionms mass of the snakeboardmr mass of the rotorJ inertia of the snakeboardJr inertia of the rotorJw inertia of the wheelsl length from the snakeboard’s center-of-mass to the wheels

O

Front foot-pad

Back foot-pad

Rotor

(a) (b)

Fig. 2: Simplified model of a snakeboard. (a) Snakeboard asviewed from top. (b) Rotor lean angle in the lateral directionof the snakeboard.

of the snakeboard. Section V presents results from numericalsimulations for various scenarios such as obstacle avoidance,achieving sharp turns and tracking desired velocities. SectionVII summarizes the work explored in this paper anddescribes future directions.

II. DYNAMICAL MODEL OF CASSIE ON A SNAKEBOARD

With the challenges described above, this sectioninvestigates the dynamical model of Cassie, snakeboard andhow they interact with one another.

A. Dynamical Model of Cassie

Cassie is a 20-dimensional bipedal robot with 10 degreesof actuation and the dynamics can be expressed as

Dqc +Cqc +G = Bτ + JTs τs + JT

c fc, (1)

where qc ∈R20 is the configuration of the robot, D ∈R20×20

is the inertia matrix, C ∈ R20×20 is the Coriolis matrix,G ∈ R20 is the generalized gravity vector, B ∈ R20×10 is theactuation distribution matrix, τs ∈R4 are the spring torques,Js is the jacobian of the spring deflections, τ ∈ R10 arethe input joint torques, fc ∈ R12 are the contact forces andJc :=

[JT

c,1 · · ·JTc,4]T ∈ R12×20 is the jacobian of the contact

positions. For later use, we define Jc :=[JT

c,1B · · ·JTc,4B]T ∈

R12×10. The configuration variables q consist of the positionof the robot, the orientation ε :=

[θc ψc φc

]T of the pelvisrepresented in Z-Y-X euler angles and the joint angles. Theseare detailed in [19]. In later sections, we will particularlyuse the yaw of the pelvis θc and the hip yaw angles denotedby qhip :=

[qhip,b qhip, f

]T corresponding to the legs on theback and front foot-pads of the snakeboard.

B. Simplified Dynamical Model of Snakeboard

For the purpose of path planning, we derive a simplifieddynamical model of the snakeboard from [9]. Figure 2depicts this model which consists of a rotor at the centerof the snakeboard to model a rider rotating their body. Theconfiguration variables of the snakeboard qs include theinertial position xs, ys, orientation θs, the angles of the frontand back foot-pads φ f and φb, and the relative angle of therotor with the snakeboard ψ . The various physical parametersof the snakeboard are mentioned in Table I. Assuming wheelsdo not slip sideways, non-holonomic constraints (2), (3) areimposed on the snakeboard,

−sin(φb +θs)xs + cos(φb +θs)ys− lθs cosφb = 0, (2)

−sin(φ f +θs)xs + cos(φ f +θs)ys− lθs cosφ f = 0. (3)

With the motion of the snakeboard restricted to levelground, the potential energy of the snakeboard remainsconstant and the Lagrangian dynamics for the snakeboard arebased solely on the kinetic energy. The equations of motionof the snakeboard [9] are then obtained as

xs =1

ms +mr

(λ1 sin(φb +θs)+λ2 sin(φ f +θs)

), (4)

ys =−1

ms +mr

(λ1 cos(φb +θs)+λ2 cos(φ f +θs)

), (5)

θs =1J

(−u1−u2−u3 +λ1l cosφb−λ2l cosφ f

), (6)

ψ =1Jr

(u1− Jrθs

), (7)

φb =1Jw

(u2− Jwθs

), (8)

φ f =1Jw

(u3− Jwθs

), (9)

where u1, u2 and u3 are the input torques at the jointscorresponding to the configuration variables ψ , φb and φ frespectively, and λ1 and λ2 are Lagrange multipliers thatarise due to the non-holonomic constraints in (2) and (3).The particular solution for λ1 and λ2 can be found in [9].

Remark 1. The variables ψ , φb and φ f correspond to thelocal configuration of the snakeboard that the rider hascontrol over. The variables xs, ys and θs correspond to theconfiguration of the snakeboard in the inertial frame. Due tothe non-holonomic constraints in (2) and (3), by modulatingthe local configuration variables, the rider can cause adesired net change in the inertial frame.

C. Contact Model between Cassie and the Snakeboard

In Section II, we used a model of the snakeboard where therotor was used as a simplification of the dynamics of the rider[9]. While this simplified model is useful for path planning ofthe snakeboard, it does not capture the true dynamics of therider. In particular, the dynamics of the rider (here, Cassie)are given by the robot dynamics in Section II-A and theinputs to the snakeboard u j, j ∈ {1,2,3} are determined by

Low-Level Joint Torque Controller

(Section IV-A)

X-Y Control(Section IV-B)

Velocity Control(Section IV-C)

Turning Control(Section IV-D)

Fig. 3: Feedback control diagram. Here qc represents Cassie’sstates and qs represents the snakeboard’s states

0 5 10

-0.05

0

0.05

0.1

-0.4 -0.2 0

-2.5

-2

-1.5

-1

-0.5

0

-0.2 -0.1 0

-0.1

-0.05

0

0.05

Fig. 4: Trajectory of the center-of-mass of the simplifiedsnakeboard model for various gaits, all with 0 initial velocity.

the contact forces between the foot and the snakeboard padsas

u1 =[0 0 1

]Σ

4i=1rc

i ×− f ic, (10)

u2 =[0 0 1

]Σ

2i=1r f p

i ×− f ic, (11)

u3 =[0 0 1

]Σ

4i=3r f p

i ×− f ic, (12)

where r f pi represents the ith location of the contact point

with respect to the foot-pads, rci denotes the ith location

of the contact point with respect to center-of-mass of thesnakeboard, f i

c denotes the contact forces at the ith contactpoint, with i = 1,2 representing the back foot-pads andi = 3,4 representing the front foot-pads of the snakeboard.

III. PATH PLANING AND GAIT GENERATION

As mentioned in Remark 1, a desired net change inthe global position and orientation of the snakeboard canbe achieved by regulating the local coordinates of thesnakeboard and the problem of trajectory planning of thesnakeboard turns into a problem of gait generation of theshape variables. We define a trajectory of the snakeboard inthe global frame as the tuple (xs(t),ys(t),θs(t)) denoting theglobal positions and orientation of the snakeboard, and a gaitas the tuple (ψ(t),φb(t),φ f (t)) denoting the shape variablesat time t ∈ [0,T ] for T > 0.

For the sake of completeness, we present below the resultsin [9] and illustrate the effects of different gaits on thetrajectories in the global frame. Consider the followingtime-varying sinusoidal inputs for the simplified modelsnakeboard in (7), (8), (9)

ui = ai sin(wit), i ∈ {1,2,3}, (13)

where the parameters of the sinusoids for various trajectoriesare presented in Table II. The drive gait (Fig. 4a) propels thesnakeboard forward or backward depending on the phase

TABLE II: Gait parameters for different gaits from [9].

Parameter Drive Gait Parking Gait Rotate Gaita1 0.3 rad 1 rad 1 radw1 1 rad/s 3 rad/s 2 rad/s

a2,−a3 0.3 rad 1 rad 1 radw2,w3 1 rad/s 2 rad/s 1 rad/s

difference between the foot-pads and the rotor. The parkinggait (Fig. 4b) results in a net displacement along the lateraldirection. The rotate gait (Fig. 4c) results in a net change inorientation of the snakeboard with very small displacementin both, x and y directions.

Remark 2. The distinguishing factor of the drive gait fromother gaits is the equal frequencies for both, the foot-padsand the rotor. In the following sections, we will particularlymake use of the drive gait presented here on the simplifiedsnakeboard model to formulate a gait planner for Cassie tofollow various trajectories.

IV. CONTROL DESIGN

Having presented the gait generation technique for thesnakeboard using the simplified model, in this section, wediscuss the low-level control strategy implemented on Cassiein order to achieve the desired trajectory while still being ableto balance on the snakeboard.

A. Low-Level Joint Controller

Our low-level feedback controller is derived from [18]which presents an optimization-based framework to obtaindesired forces f d

c =[

f dc,1

T · · · f dc,4

T ]T ∈ R12 at the fourcontact points that stabilizes the center-of-mass position rc ∈R3 and velocity rc of the robot as well as the orientation ε

and rotational velocity ε of the pelvis to desired values rdc ,

rdc , εd and εd . This is achieved by considering a fictitious

wrench Fcom ∈ R6 at a frame coincident with the center-of-mass of the robot and parallel to the orientation of the pelvis,

Fcom =

[mcge3−Kp(rc− rd

c )−Dp(rc− rdc )

R(−2(

δ I+ ξ

)Krξ −Dr

(ω−ωd

))] , (14)

where e3 =[0 0 1

]T , R is the equivalent rotation matrixrepresentation of the orientation of the pelvis given by R =Rz(θc)Ry(γc)Rx(φc), with Rz, Ry and Rx denoting the rotationsabout the Z, Y and X axes respectively. The rotation matrixRd corresponding to the desired orientation can be similarlyobtained. The terms ξ and δ denote the vector and scalarpart of the quaternion corresponding to the orientation errorRdT R. Additionally, ω and ωd denote the actual and desiredbody angular velocities of the pelvis respectively, which canbe obtained from the euler angles and their velocities. Thedesired height rd

c with respect to the snakeboard is kept at aconstant value and the desired yaw of the robot’s pelvis withrespect to the snakeboard is a sinusoidal function as in (13).

The center-of-mass wrench Fcom can be transformed toequivalent contact forces f d

c through the grasp map Gc and

0 10 20 30 40

0

0.1

0.2

0 10 20 30 40

-0.2

0

0.2

Fig. 5: Results for velocity tracking simulation in SectionV-A. Top: Velocity tracking results with the Cassie-snakeboard system initially at rest. Middle: Foot-pad anglesof the snakeboard. Bottom: Center-of-mass position of thesnakeboard follows a nearly straight line.

wrench basis W as, Fcom = GcW f dc , where the wrench basis

W is required to transform a force f dc,i at a contact point

to an equivalent wrench F ic =

[f dc,i

T 0T3×1]T

. The desiredcontact forces can then be obtained by finding the minimizerof ‖Fcom − GcW f d

c ‖2. However, in order to oscillate thefoot-pads of the snakeboard as in (13), we require the legsof Cassie to follow a sinusoidal trajectory, in addition tomaintaining a desired center-of-mass position and orientationof the pelvis. We also require that the feet do not slip onthe foot-pads. We achieve this by formulating the feedbackcontrol as the following optimization problem,

minf dc ,τ‖Fcom−GcW f d

c ‖2WF

+‖τhip− τdhip‖2

Wτ+‖τ + JT

c f dc ‖2

Wδ

s.t. f dc ∈K f ric, (15)

− τ ≤ τ ≤ τ,

where τhip ∈R2 are the torques at the hip yaw joints, τ ∈R10

denotes the joint torque limits on Cassie, K f ric correspondsto the linearized friction cone constraints [20] and τd

hip isgiven by the linear feedback term,

τdhip =−Khip(qhip−qd

hip)−Dhip(qhip− qdhip), (16)

where qdhip =

[qd

hip, f qdhip,b

]T∈ R2 and qd

hip are desiredsinusoidal trajectories for the hip joint angles and velocitieson the front and the rear foot-pads, Khip and Dhip areappropriate feedback gains. The term ‖τ + JT

c f dc ‖2

Wδin

the cost function captures the quasi-static relationship τ =−JT

c f dc between the joint torques and the contact forces.

Remark 3. As mentioned earlier, due to the lack of armsand an upper torso, Cassie has limited control over theyaw momentum which limits the types of trajectories and

behaviors that Cassie can execute with the snakeboard. Inthe following sections, we will specifically use the drive gaitpresented in Section III. In addition, while (13) considerssinusoids for the input torques ui of the simplified snakeboarddynamics, in the next sections, we will instead considersinusoidal trajectories for the desired hip angles qd

hip(t) anddesired pelvis yaw θ d

c (t). We also make an assumption thatthe feet do not slip on the snakeboard foot-pads. With thisassumption, the foot-pads follow the hip joint trajectories.

B. Snakeboard X-Y controller

To achieve a desired displacement in the XY plane, weconsider a modified version of the drive gait. In particular,we consider the following desired trajectories for the hipjoints and pelvis yaw,

qdhip, f (t) = c+asin(wt), qd

hip,b(t) =−asin(wt), (17)

θdc (t) = asin(wt), (18)

with c =−Kx(xs−xds )−Dx(xs− xd

s ), where xds represents the

desired x location. This controller prevents the board fromdrifting too far from the desired x-direction.

C. Velocity Controller

Velocity control is accomplished by regulating theamplitude of the sinusoids in (17)-(18) given by theproportional feedback law,

a =−Kv(vs− vds ), (19)

where vs =√

x2s + y2

s represents the magnitude of the velocityof the snakeboard.

D. Turning Controller

The turning controller maintains a desired heading angleθ d

s of the snakeboard. We consider the following gait for thedesired hip angles qd

hip,

qdhip, f = c+asin(wt), qd

hip,b =−c−asin(wt), (20)

where c =−Kθ (θs−θ ds )−Dθ (θs− θ d

s ).To account for sharp turns, Cassie would need to lean in

the direction of the turn to ensure stability and balance on thesnakeboard. To further analyze this, we consider an invertedpendulum model in Fig. 2 that represents Cassie’s center-of-mass. Here, Fs and Fn denote the tangential and normalforces acting at the contact points, and Fc =

mv2

R denotes thecentripetal force at the center-of-mass.

Using a comparable model to the snakeboard studied by[21], the radius of curvature of the trajectory R can becalculated as,

R =2l(

tanφ f − tanφb)

cosω, (21)

ω = arctantanφb + tanφ f

2, (22)

where ω represents the slip angle at the center-of-mass ofthe board and l represent the length of the center-of-massof the snakeboard to the foot-pad. Summing up the moment

-4 -2 0 2

0.5

1

1.5

2

2.5

0 10 20 30 40

-0.4

-0.2

0

0.2

0.4

(a)

(b)

Fig. 6: Results for tracking a circular path in Section V-B.(a) Foot-pad angles of the snakeboard. (b) Center-of-massposition of the snakeboard.

about point O in Fig. 2 the desired lean angle θ dl for Cassie

is given by

θl = arctanv2

gR. (23)

To achieve the desired lean angle θl , we consider thefollowing desired center-of-mass position with respect to thesnakeboard rd

c for Cassie in (14) as,

rdc = ∆z

sinθl cosθssinθl sinθs

cosθl

, (24)

where ∆z is the difference between a nominal desired heightof Cassie from the ground and the height of the snakeboard’sfoot-pads from the ground.

V. SIMULATION RESULTS

Having presented the dynamics of the Cassie-snakeboardsystem and a feedback controller for regulating the inertialposition and orientation, we now present results fromnumerical simulation for various scenarios.

A. Velocity Tracking

In this section, we consider regulating the velocity ofthe Cassie-snakeboard system while following a straightline. This is achieved by the control strategies presented inSection IV-B and Section IV-C. Fig. 5 illustrates the resultsof velocity tracking of the forward velocity of the Cassie-snakeboard system.

0 0.5 1 1.5

-0.02

-0.01

0

0.01

0.02

-10 -5 0

-2

-1

0

1

2

Fig. 7: Numerical simulation results for the simplifiedsnakeboard model moving (a) uphill and (b) downhill.

B. Turning Controller - Circular Path

The turning controller utilizes both, the velocity andthe turning controllers. Fig. 6 illustrates the results froma numerical simulation of the turning controller. In thisparticular case, we consider the desired heading angle to beθ d

s (t) = 0.2t + θ0, t > 15s where θ0 = π/2. For t ≤ 15 weuse the velocity controller to follow a straight path and buildup speed.

C. Turning Controller - Sinusoidal Path

We consider a sinusoidal trajectory that requires Cassieto make sharp turns without slipping and illustrate theimportance of leaning during sharp turns. In this example,we consider an initial velocity of 0.8m/s for the Cassie-snakeboard system and a desired heading angle θ d

s =0.8sin t +θ0 where θ0 = π/2.

For the case without leaning into a turn, Cassie slipswithin a few seconds as can be seen in Fig. 8 (top-right),which shows that the ratio between the sum of the horizontalforces over the normal force exceeded the coefficient of staticfriction. However, for the case where the robot was able tolean, Cassie is able to maneuver itself into sharp turns whilestill ensuring the friction constraints are satisfied, as shownin Fig. 8 (top-left).

D. Obstacle Avoidance

For avoiding obstacles in the task-space, we begin bydefining a path that geometrically avoids the obstacles. Then,by utilizing the XY controller, we can follow the trajectoryto avoid obstacles. Fig. 9 shows a simulation of the Cassie-snakeboard system avoiding two different obstacles in theshape of a sphere with a radius of 0.2m. To achieve this, weconsider the piece-wise function for the desired x positionas a function of y,

xds = 0.3sin(ys− y0), (25)

where the particular values of y0 are obtained by consideringthe position of the obstacles. In this particular case, Cassie’sinitial velocity is equal to 0.2m/s.

VI. FUTURE WORK

As part of future work, we plan to implement the proposedcontroller on hardware. We also seek to explore robots withan upper torso and arms, like Digit 2, to broaden the range

2https://www.agilityrobotics.com/meet-digit

0 5 10 15

0

0.5

1

0 5 10 15

-5

0

5

0 2 4

0

0.5

1

0 2 4

-2

0

2

23

Fig. 8: Simulation results for sinusoidal trajectory in Sec.V-C with (left column) and without (right column) leaninginto sharp turns.

Fig. 9: Center-of-mass position of the snakeboard whileavoiding obstacles (in red).

of achievable motions. Another potential future direction isto analyze the problem of negotiating inclines. Towards thisgoal, we analyzed the dynamics of the simplified model ofthe snakeboard on surfaces of a constant incline angles. Withthe assumption that the ground makes a constant angle α

with the x−axis, the Lagrangian of the snakeboard can bewritten as

L =12(ms +mr)

(xs

2 + ys2)+ 1

2Jθ

2s +

12

Jr(ψ + θs

)2+

12

Jw

((φb + θs

)2+(φ f + θs

)2)− (ms +mr)gxs sinα, (26)

where g denotes the acceleration due to gravity. Fig. 7illustrates the drive gait from Section III for going up anddownhill with the simplified snakeboard dynamics. As partof future work, we plan to investigate navigation on severeinclines and dynamic hybrid motions like flips and jumpswith the snakeboard.

VII. CONCLUSION

In this paper, we presented a gait generation technique andfeedback controller for a bipedal robot to autonomously ridean unpowered wheeled platform called Snakeboard, which isa steerable variant of a Skateboard. Our proposed controlleris able to achieve sharp turns, navigate around an obstaclecourse and follow desired trajectories in the task space.

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