System Design of the Ultra Mobility Vehicle: A Driving, Balancing, and Jumping Bicycle Robot

Benjamin Bokser; Daniel Gonzalez; Aaron Preston; Alex Bahner; Annika Wollschläger; Arianna Ilvonen; Asa Eckert-Erdheim; Ashwin Khadke

Figure 1: The Ultra Mobility Vehicle (UMV) and its athletic repertoire. ( A ) Diagram of UMV, a bicycle-based robot with five actuated degrees of freedom [Links (green) and subcomponents (purple)]. It has steering and rear-wheel drive actuators for basic ground mobility. The design concentrates most of the robot’s mass in the Head , which connects to the Bike through a spatial linkage. This linkage consists of the Neck and two tie rods. Powerful actuators in the Head work through the linkage to let the robot “throw” its mass around, enabling dynamic behaviors. Composite images of ( B ) a front flip, demonstrating high pitch angular momentum and modulation of inertia via body tucking, ( C ) rear-wheel hopping, where the robot maintains balance like a single-legged hopper, ( D ) an autonomous table jump sequence, where the robot accelerates, vaults onto a 1-meter platform, traverses it, and lands stably.

List of Movies 1 UMV combines the bicycle form with legged agility, allowing for athletic motions, including: (1) track-standing, in which the robot balances in place using only wheel and steering actuation; (2) backward driving, (3) “shimmy-turning,” in which the robot lifts the front wheel to yaw in place about the rear wheel, (4) lateral hopping on a single wheel, (5) front flipping, and (6) high-clearance table jumping.

Figure 2: Kinematic architecture and actuation strategy. ( A ) Side view showing joint layout. Joints

q_{h}

,

q_{l}

, and

q_{r}

actuate the spatial linkage, allowing the Head to shift its mass relative to the Bike link. The design parameter

\hat{\psi}

represents the fixed angle of the out-of-plane joint

\phi

axis. ( B ) Detailed view of the spatial mechanism and actuator placement. Actuators

A_{0}

through

A_{3}

are remotized to the Head to maximize the center of mass height and minimize leg inertia for jumping.

A_{0}

and

A_{1}

are mechanically coupled to drive the

\phi

joint, providing lateral authority for single-wheel balancing.

Figure 3: Positions, footstep locations, and headings over a roughly 12-second period of lateral hopping on hardware.

p_{\text{CoM}}

shows the oscillation of the whole-body center of mass throughout the hopping motion. The traces at ground level (

p_{\text{clearance}}

) indicate the lowest point of the rear wheel in both flight and stance. These visualize a learned stabilization strategy where the rear wheel rolls backward and forward during the stance phase to maintain balance, analogous to a unicycle.

Figure 4: Energetics and repeatability of high-clearance jumping. ( A ) System performance during a 1-meter table jump. The top plot shows the CoM height (

h_{\text{CoM}}

) and rear wheel clearance (

h_{\text{clearance}}

). The vertical dashed lines mark the high-impulse lift-off and landing impact events. The bottom plots illustrate the electrical demand; the system draws peak power (approx. 4.5 kW) immediately prior to lift-off, causing a significant voltage sag, while landing impacts briefly drive the actuators into regeneration (negative power). ( B ) Spatial repeatability of the rear wheel trajectory (

p_{\text{clearance}}

) across 15 consecutive autonomous jumps. The tight clustering of trajectories during the ascent phase demonstrates the precision of the learned policy, with increased variance occurring only post-impact during the drop-landing.

Figure 5: Angular momentum conservation during a front flip. This data trace illustrates the physics of the flip maneuver shown in Fig. 1B. Following lift-off (first vertical dashed line), the robot actively tucks its body, drastically reducing the pitch inertia

I_{yy}

(middle plot, black line). This reduction in inertia facilitates a rapid increase in pitch angular velocity

\omega_{y}

(bottom plot, black line), peaking at approx. 17 rad/s, allowing the robot to complete the rotation before extending for impact (second vertical dashed line). Shown in the bottom plot is the angular velocity of the Bike link.

Figure 6: Design space exploration for jumping morphology. A qualitative overview of the kinematic topologies evaluated during the design phase. Morphologies were assessed based on their theoretical capacity for vertical jumping, including the ratio of extended height to crouched height per unit of link length. Concepts ranged from simple prismatic legs (A) to complex multi-linkage systems (H, I). Topology (B) was selected for UMV as it offered the optimal trade-off between stroke length, mass distribution, and mechanical complexity.

Figure 7: Mass distribution sensitivity and optimization of transmission ratios. ( A ) Sensitivity analysis of link mass on jump height. We varied each link mass while keeping the other masses at their nominal value (“Current Design”). The slope for the Head (blue) is shallower than the slopes for the Bike (green) and Neck (yellow), which indicates that remotizing mass to the top of the robot has a smaller penalty on jumping performance. The current design is already the result of a concerted effort to minimize the mass of the lower links within practical limits. ( B ) Gear ratio optimization landscape. The heat map displays jump height as a function of the gear ratios for actuators

A_{0}

and

A_{1}

(

GR_{\alpha}

) and actuators

A_{2}

and

A_{3}

(

GR_{\beta}

). The star indicates the selected ratios, chosen to maximize performance while remaining within the “Practical limits” (hatched area) imposed by pulley diameter constraints and gearbox complexity.

Figure S1: A reduced 2D model used for vertical jump height optimization.

Figure S2: An early study of the effect of gross robot scale on clearance height and contact ratio. A “scale” of 1.0 corresponds to a robot with a Neck length of 1 meter. With increasing scale, jump height increases up until the actuators are no longer able to provide the torque required to build upward momentum. We compared the use of a single AK10-9 actuator to drive joint

q_{h}

versus the use of a set of coupled AK10-9 actuators for the same purpose. This study used the actuator’s original gear ratio of 9:1, and the relationship between link length, mass, and moment of inertia was determined by approximating links as cylinders.

Figure S3: Communications and power architecture. All actuators (

A_{0}

through

A_{5}

) have encoders built-in. More information on the mapping of actuators to joints can be seen in Table S2 . Because each RL policy requires observations of one of the two bodies, we mount one IMU on the Head and another on the Bike link. With only one IMU, the angular and linear velocities of the other body would become a function of the (noisy) derivative of the joint position measurements, decreasing the overall accuracy of the observations.

Figure S4: Sensitivity of balance controllability to design parameter changes for an extra DoF. ( A ) Variation in minimum required control effort (( 3 )) during wheelie balance with variation of the axis orientation

\hat{\psi}

of joint

\phi

as depicted in Fig. 2 . The optimal value of

\hat{\psi}

is such that the axis of joint

\phi

roughly intersects the rear axle. ( B ) Comparison of the minimum required control effort of the current morphology (without extra DoF) to that of a 6-DoF morphology (with extra DoF) shows that it would require additional control effort in balancing and is not necessary.

$A_{i}$	Actuators
$\omega$	Angular velocity of the bike frame
$q_{h}$	Joint between the Head and Neck links
$q_{l}$	Right arm joint
$q_{r}$	Left arm joint
$q_{s}$	Steering joint
$q_{w}$	Rear wheel joint

Table S1: Nomenclature .

$k_{p}$ , $k_{d}$	PD gains
$\tau$	Torque setpoint command
$v_{c}$	Base forward vel. and heading command
$\Theta$	Phase variable
$g$	Gravity vector
$o_{c}$	Observation vector
$a$	Actions vector

Table 14

Actuator	P/N	Gear	Max Torque	Max Speed	Driven
		Ratio	(Nm)	(rad/s)	Joint(s)
$A_{0}$	AK10-9	297:22	72	29.4	$q_{r}$
$A_{1}$	AK10-9	297:22	72	29.4	$q_{l}$
$A_{2}$ + $A_{3}$	AK10-9	450:22	218	19.4	$q_{h}$
$A_{4}$	R80	13:2	26	74	$q_{w}$
$A_{5}$	R60	38:14	6.25	160	$q_{s}$

Table S2: Actuator Specifications for UMV . See Fig. 2 B for placement on the robot.

List of Movies S1 Continuous autonomous table jumping. The robot executes a continuous routine of fifteen autonomous jumps onto and off of a 1-meter platform without intervention. This experiment illustrates the policy’s repeatability and the hardware’s endurance under sustained loads. The trajectories of this motion are analyzed in Fig. 4 B.

List of Movies S2 Initial self-contained field demonstrations. The robot is shown operating outdoors along a biking trail (Allmendtrail, Zürich). The UMV robot performs essential locomotion tasks — including balancing, turning, and acceleration — using fully onboard power, state estimation, and controls.

System Design of the Ultra Mobility Vehicle: A Driving, Balancing, and Jumping Bicycle Robot

Abstract

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