Source-linked AI summary
A Long-Legged, Direct-Drive Monopedal Robot Achieves Exceptional Jump Height
Gihyeok Na, Justin K. Yim
TL;DR
Direct-drive jumping avoids elastic energy storage, but its jump power is limited by the actuator’s instantaneous output. This paper pairs a long leg stroke with a variable-mechanical-advantage fabric-wrap transmission and demonstrates a 7.6 m jump, the highest yet reported for an electrically actuated spring-free system.
Problem
Direct-drive jump power cannot exceed the actuator’s instantaneous limit, motivating a design that maximizes leg stroke and power-to-mass ratio without adding elastic elements.
Source: A. Motivation · p. 1, C. Jumping Actuation Methods · p. 2Method
A fabric-wrap direct-drive transmission provides variable mechanical advantage through the stroke, and its telemetry shows power settling near the motor’s peak and remaining there.
Source: B. Contribution · p. 2, A. Jump Height · p. 6Results
7.6 m: the robot achieved the highest jump yet demonstrated by a direct-drive electrically actuated robot without mechanical energy storage, and its vertical jumping agility was 5.30 ms−1, highest among electrically actuated robots of any transmission type.
Source: A. Jump Height · p. 6, §IV · p. 7Takeaways & Limitations
The reported jump height and vertical jumping agility expand the demonstrated envelope of electrically actuated, spring-free jumping robots.
Source: §IV · p. 7For the tilted jump, aerial stabilization was not attempted because the robot was already near the module’s in-flight recovery limit at liftoff.
Source: C. Tilted Jump · p. 7
Abstract
from arXiv · showhide
We demonstrate a jumping robot that reaches high (7.6 m) and fast (190 ms stance time) jumps from a single long leg driven by a direct-drive transmission, without elastic energy storage. At 281 g, it achieves the highest jump yet reported for an electrically actuated, spring-free system. The leg uses a new fabric-wrap transmission that provides a variable mechanical advantage, keeping a small electric motor near its peak power output through the stroke while bracing the long, lightweight leg against buckling. A balancing module at the top of the leg uses small propellers to control the leg's orientation on the ground and in the air, where the long leg provides a large moment arm for the control torques. The robot is validated outdoors with vertical jumps, attitude control on the ground and in flight, and tilted jumps.
I. INTRODUCTION
Jumping can help terrestrial locomotors navigate challenging environments, and jump height and frequency capture distinct aspects of that performance. Vertical jumping agility combines them to describe the maximum ascent rate achievable by hopping up steps.
I. INTRODUCTION
- Jump height is the COM’s vertical displacement from motion start to apex, and jump frequency is defined from stance duration and flight time.Stance duration is ground-contact time; flight time runs from liftoff to the apex.Source: A. Motivation · p. 1
- Vertical jumping agility multiplies jump height by jump frequency and can be read as the maximum ascent rate over steps spaced by jump height.Jump height has also been compared after scaling by body length, power, and time.Source: A. Motivation · p. 1
- Jump height expands a robot’s ability to cross large obstacles, while rapid, powerful jumps can support faster traversal.The paper defines jump height as the COM’s vertical displacement from motion start to the apex.Source: A. Motivation · p. 1
B. Contribution
The paper introduces a fabric-wrap transmission for a direct-drive monopedal jumper and demonstrates a 7.6 m jump. It motivates the design by contrasting elastic actuation’s stored-energy benefits with the direct-drive strategy of maximizing leg stroke and power-to-mass ratio.
B. Contribution
- The fabric-wrap transmission pairs a long leg stroke with variable mechanical advantage, while the balancing module enables attitude control and tilted jumps.The transmission provides variable mechanical advantage without added gearing.Source: B. Contribution · p. 2
- 7.6 m: the robot demonstrates a jump with a fabric-wrap direct-drive transmission and no added gearing for variable mechanical advantage.The work also integrates a balancing module for attitude control and tilted jumps.Source: B. Contribution · p. 2
C. Jumping Actuation Methods
- Elastic systems trade added mechanisms and complexity for stored energy: series springs can boost instantaneous output power, while parallel springs have achieved the highest reported jump heights.Series-elastic systems can lengthen stance to charge the spring; parallel-elastic systems add winding and triggering mechanisms and make mid-jump energy modulation more complex.Source: C. Jumping Actuation Methods · p. 2
- The direct-drive design instead maximizes leg stroke and actuator power-to-mass ratio, the two remaining levers identified for a power-limited actuator.The passage describes jump height scaling with total mass, leg stroke, and peak actuator power.Source: C. Jumping Actuation Methods · p. 2
- Direct-drive actuation omits elastic elements, winding, and triggers, yielding a simpler, lighter powertrain and shorter stance than charging a spring requires.Rigid coupling also allows continuous ground-reaction-force commands and high-bandwidth force control; motor current alone could estimate leg force.Source: C. Jumping Actuation Methods · p. 2
D. Related Works
Prior jumping robots use elastic storage or direct drive, with different height, complexity, and continuity trade-offs. The paper situates its monopedal design among electrically actuated systems and compares them by mass, leg stroke, jump height, and vertical jumping agility.
D. Related Works
- Salto and Salto-1P, with 14.4 cm leg length and 98 g mass, achieve a standing vertical leap of 1.25 m using series-elastic power modulation; Ascento, a 10.4 kg bipedal wheeled-legged robot, reaches a maximum jump height of 0.4 m.Source: D. Related Works · p. 2
- Parallel-elastic designs include a 32 m jump using a 1000:1 reduction and latch, but require about 120 s on the ground to recharge between jumps.Other examples include 3.6 m hopping with high continuity and a 1.5 m JumpRoACH jump using springs and latex bands.Source: D. Related Works · p. 3
- Direct-drive quadrupeds include Stanford Doggo’s 1.14 m vertical jump, but these general-locomotion platforms have relatively short leg strokes and high mass.The passage also cites Minitaur and MIT Cheetah 2 as direct-drive or quasi-direct-drive platforms.Source: D. Related Works · p. 3
- Among height-focused direct-drive monopeds, RAMIEL reaches 1.6 m and a rack-and-pinion robot reaches 0.59 m; both use minimal, rod-like legs without linkages.The comparison table covers electrically actuated robots’ mass, leg stroke, jump height, and vertical jumping agility.Source: D. Related Works · p. 3
A. System Overview
The 281 g robot combines a long structural leg and a top-mounted balancing module with a fabric-wrap transmission. The wrap’s changing mechanical advantage keeps the motor near its peak-power range over more of the stroke while also supporting the leg.
A. System Overview
- The long carbon-fiber leg connects a lower body carrying the jump actuator to an upper balancing module, with their combined center of mass on the leg axis.Source: A. System Overview · p. 3
- The lightweight tube’s low bending stiffness allows it to vibrate with the balancing module active unless the tripod constrains its base.The tripod also suppresses vibration when the balancing module is active.Source: A. System Overview · p. 3
- 281 g is the total system mass.Source: A. System Overview · p. 3
B. The Fabric-Wrap Transmission
- The fabric-wrap transmission’s changing radius decreases mechanical advantage as the leg extends, keeping the motor near its peak-power range over more of the stroke without extra gearing.The helical wrap also braces the long leg against buckling and damps bending vibration.Source: B. The Fabric-Wrap Transmission · p. 4, Figure 4 · p. 4
C. The Balancing Module
The top-mounted propeller module controls the leg’s lean during ground contact and flight. Its control model changes at liftoff, from rotation about the foot to rotation about the robot’s center of mass.
C. The Balancing Module
- A maximum net thrust of 0.50 N, about 18% of robot weight, acts through a roughly 1973 mm stance moment arm for orientation control.Source: C. The Balancing Module · p. 5
- During contact, the planted foot and supporting tripod define an inverted-pendulum system, and the control law cancels gravity while treating tripod torque as a bounded disturbance.Source: C. The Balancing Module · p. 5
- After liftoff, the robot rotates about its center of mass without a gravity moment, and the module switches to aerial gains as the thrust acts through the COM-to-module moment arm.Source: C. The Balancing Module · p. 5
- The module can hold the leg upright or at a commanded lean up to 15°, and cuts thrust beyond a 60° tilt as a safety measure.Source: C. The Balancing Module · p. 5
D. Experiment Setup
Outdoor vertical jumps were recorded with calibrated camera geometry, and the robot was commanded to balance upright through flight. Tilted jumps used a lean setpoint before takeoff but no upright-attitude command after liftoff.
D. Experiment Setup
- Two 120-FPS GoPro cameras and suspended meter sticks provided the geometry for measuring motion during open-field vertical jumps.Source: D. Experiment Setup · p. 5, Figure 6 · p. 6
- In vertical jumps, the robot balanced upright before takeoff and the balancing module maintained upright attitude through flight until touchdown.Source: D. Experiment Setup · p. 6
- For tilted jumps, the balance-angle setpoint was shifted before takeoff, and upright attitude was not commanded after liftoff.Source: D. Experiment Setup · p. 6
A. Jump Height
The robot reached approximately 7.6 m in a 2.5 s jump, with horizontal displacement below 1.6 m in both axes. Actuator power settled near its peak and stayed there through the stroke, as intended by the fabric-wrap transmission.
A. Jump Height
- 7.6 m was the robot’s maximum jump height; the jump lasted about 2.5 s, with horizontal displacements under 1.6 m in both axes.The trajectory was reconstructed in 3D by stereo triangulation.Source: A. Jump Height · p. 6
- For computing VJA, the authors use body height as COM height because the body and balancing module are nearly co-located and the leg tube’s mass offset is negligible.The body is 192 g, the balancing module 55 g, and the leg tube 27 g, out of 281 g total.Source: A. Jump Height · p. 6
- Mechanical power settled near its peak after an initial ramp and remained there for the rest of the stroke.The authors identify this as the intended effect of the fabric-wrap transmission.Source: A. Jump Height · p. 6
B. Attitude Control
The balancing module controls attitude during both stance and flight: it keeps the leg upright against disturbances, sets takeoff lean, and works to stabilize the robot in the air. Ground commands were tracked, while aerial attitude deviations were reduced but not fully settled.
B. Attitude Control
- During stance, the balancing module rejects disturbances such as wind and sets the lean angle for the jump.The measured roll and pitch followed commands stepped to 15° and returned to level.Source: B. Attitude Control · p. 6
- In flight, the controller switches from ground to aerial gains after liftoff and reduces attitude deviations, but does not fully settle them.The COM remains close to the thrusters because body retraction toward the foot in flight is not implemented, limiting use of the long leg’s moment arm.Source: B. Attitude Control · p. 6
C. Tilted Jump
Leaning the leg with the balancing module lets the robot steer its jump direction during stance, potentially placing touchdown over successive jumps while the main actuator sets jump height independently. In an outdoor tilted-jump test, it leaned about 20° and lifted off approximately 190 ms after the jump command; aerial stabilization was not attempted.
C. Tilted Jump
- Stance leaning with the balancing module can steer jump direction and potentially place touchdown over successive jumps, while the main actuator sets jump height independently.This is presented as a potential capability for directional multijump locomotion.Source: C. Tilted Jump · p. 6
- 190 ms after the jump command, the robot lifted off after reaching a lean of about 20° in the outdoor tilted-jump test.The sequence began with the robot balancing upright and then leaning as the setpoint changed.Source: C. Tilted Jump · pp. 6–7
- Aerial attitude stabilization was not attempted because the robot was already near the module’s recovery limit at liftoff, and body repositioning to lengthen the moment arm is not implemented.The tilted jump is described as a step toward directional multijump locomotion.Source: C. Tilted Jump · p. 7
IV. CONCLUSION AND FUTURE WORK
The robot demonstrated high, rapid jumping with direct-drive actuation, reaching 7.6 m and a vertical jumping agility of 5.30 m s−1. The work validates the transmission and outdoor control, while continuous hopping remains future work.
IV. CONCLUSION AND FUTURE WORK
- The robot achieved 7.6 m high jumps, highest yet demonstrated by a DD electrically actuated robot without mechanical energy-storage elements, and highest vertical jumping agility, 5.30 ms−1, among electrically actuated robots of any transmission type.Source: §IV · p. 7
- Similar designs could produce larger jumps on the Moon, where lower gravity may allow obstacle crossing or overhead imaging in an atmosphere-less environment.These are proposed applications, not demonstrations in this work.Source: §IV · p. 7
- The work validated fabric-wrap transmission power output and jumping performance, balancing-module control authority on the ground and in the air, and component durability through outdoor jumps and landings.Reliable in-air body repositioning and control for continuous hopping are future work; hopping was not demonstrated.Source: §IV · p. 7
- The authors suggest the fabric-wrap propulsion may suit other fast-launch, low-mass behaviors, including self-launching fixed-wing drones.They also identify scaling to higher masses and different length scales as a topic for future exploration.Source: §IV · pp. 7–8