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Make it Walk: Computational Design of LEGO Walkers
Siqi Li, Fancheng Gao, Chi-Wing Fu, Peng Song
TL;DR
Existing LEGO walkers are mostly based on single-actuator mechanisms with fixed gaits, limiting versatility. This paper co-designs walker morphology and control using gear-linkage legs and independent motors with synchronized timing. The approach designs varied gaits and appearances, and two walkers were fabricated to demonstrate stable real-world locomotion.
Problem
Reused single-actuator walking mechanisms give LEGO walkers stable but few fixed gaits, limiting their versatility and expressiveness.
Source: §1 · p. 1Method
A computational approach co-designs walker morphology and control, using gear-linkage mechanisms for leg trajectories and independently driven legs with synchronized timing.
Source: §1 · p. 2Results
The approach designs LEGO walkers with varied gaits and appearances, and two fabricated walkers demonstrated stable locomotion and walking gaits in the real world.
Source: §7 · p. 9Takeaways & Limitations
Decoupling leg trajectory and timing control supports a relatively simple morphology and controller for stable walking with varying gaits.
Source: §7 · p. 9The current approach is limited to statically stable creeping gaits, restricting the range of achievable gaits.
Source: §7 · p. 9
Abstract
from arXiv · showhide
LEGO walkers are walking automata constructed from modular LEGO Technic bricks. They exhibit intriguing locomotion and are also highly reconfigurable through the modular Technic bricks, making them widely applicable in education, recreation, and robotics research. However, existing LEGO walkers are designed mostly by reusing existing single-actuator walking mechanisms. Although the locomotion is stable, their fixed walking gaits limit their adaptability and versatility. This paper presents the first computational solution capable of designing LEGO walkers that not only walk stably, but also support a variety of walking gaits. Our idea is twofold. First, we control the foot motion trajectory of each leg mechanically via a specifically-designed gear-linkage mechanism, in which we incorporate a pair of 3D-printed non-circular gears to work with a LEGO Technic mechanism. Second, we drive each leg by an independent motor and synchronize the timings of multiple leg motions via a simple yet adaptable control algorithm, enabling stable and versatile locomotion. Importantly, we take this modeling as a foundation to co-design the morphology and control of the LEGO walkers to meet the target locomotion and appearance. Leveraging our approach, we created a variety of LEGO walkers, demonstrating various walking gaits and appearances, and fabricated some of them to show their locomotion capability in the real world.
1. Introduction
Existing LEGO walkers can walk stably but are largely built from reused mechanisms with fixed gaits, limiting versatility. The paper proposes mechanically controlling each leg’s trajectory and electronically synchronizing leg timings, then co-designing walker morphology and control for target gaits and appearance.
1. Introduction
- Reused linkage mechanisms such as Klann and Jansen’s provide stable walking but constrain LEGO walkers to a few fixed gaits, limiting versatility and expressiveness.Existing examples also rely on bulky and complex mechanisms.Source: §1 · p. 1, Figure 2 · p. 2
- Designing stable walkers with varying gaits requires selecting mechanical parts, their connections and actuation, as well as geometry, layout, and control.The paper frames the large combined design space as a second challenge.Source: §1 · pp. 1–2
- A gear-linkage mechanism with 3D-printed non-circular gears controls each leg’s foot trajectory, while independent motors and electronic synchronization coordinate leg timing.The approach decouples trajectory and timing control and describes the resulting morphology as simple and lightweight.Source: §1 · p. 2
- The computational approach co-designs walker morphology and control to meet a target gait and appearance, then produces brick assemblies, gear shapes, assembly instructions, and motor control.The authors report designing quadruped and hexapod walkers and physically realizing several designs.Source: §1 · p. 2
2. Related Work
Related work spans computationally designed walking automata, walking robots, and LEGO Technic models. This paper focuses on fabricable LEGO walkers that support stable walking with varying gaits.
Walking automaton design
- Computational walking-automata research includes mechanisms for mid-air motion and methods for stable ground walking, including user-created automata optimized from predefined linkage templates.Examples of mid-air designs include mechanical characters [CTN∗13] and compliant mechanical systems.Source: §2 · p. 2
- Prior ground-walking automata use predefined template linkages or a composite cam-follower mechanism, with the latter designed for a fixed gait.Bharaj et al. [BCT∗15] use template mechanisms; Cheng et al. present a six-leg automaton.Source: §2 · p. 2
Walking robot design
- Walking robots support varied gaits but typically require many actuators, making fabrication expensive and control complex; LEGO Technic’s low stiffness and joint clearance make it uncommon for such robots.The paper studies LEGO walkers as inexpensive, easy-to-control systems for stable walking with varying gaits.Source: §2 · p. 3
LEGO Technic design
- Prior LEGO Technic design work computes models from sketches, while the authors report no known research on constructing LEGO Technic walkers.Earlier LEGO model research mainly addresses static structures made with non-Technic bricks.Source: §2 · p. 3
3. Problem Statement and Overview
The design problem takes a LEGO body frame and a target gait as inputs and produces a fabrication-ready walker. The approach models each leg as an independently actuated gear-linkage mechanism, then optimizes morphology and control.
3. Problem Statement and Overview
- Inputs are a body frame with a plane for leg attachment and a walking gait specified by a target foot locus and footfall pattern.The footfall pattern specifies the timing and sequence of each leg’s ground contact.Source: §3 · p. 3
- The output is a fabrication-ready walker meeting gait and appearance requirements, with leg geometry and fabrication package, leg layout, and coordinated servo trajectories for balance.The fabrication package includes LEGO Technic assemblies, non-circular gear profiles, and step-by-step assembly instructions.Source: §3 · p. 3
- Each leg is modeled as a gear-linkage mechanism driven by an independent actuator, and optimization co-designs walker morphology and control.The method searches for a design that meets the specified walker requirements.Source: §3 · p. 4
4. Modeling LEGO Walkers
The section models LEGO walkers through a geared leg mechanism, a body-mounted arrangement of actuated legs, and criteria for statically stable creeping gaits.
4.1. Modeling Leg Mechanisms
- A geared five-bar linkage uses non-circular gears to reduce its two degrees of freedom to one while generating diverse foot trajectories.Link geometry uses integer coordinates for LEGO Technic constraints; the follower angle is modeled as a function of the driver angle, with K=1 used for cyclic gaits and singular configurations avoided.Source: §4.1 · pp. 4–5
4.2. Modeling and Actuating LEGO Walkers
- A walker combines a target body frame with N legs sharing a mechanical design but allowing different mounting poses and actuation trajectories.Legs are synthesized in local planes and mounted through frame transformations, including mirror transformations; each leg’s driver angle trajectory is chosen to satisfy stable-gait kinematic requirements.Source: §4.2 · p. 5
4.3. Stable Walking Gaits
- Stable creeping gaits use support and transfer phases, with stability requiring the center-of-mass projection to remain inside the grounded-feet support polygon throughout the cycle.The gait description includes step height, step width, and duty factor; the static stability margin is the distance from the COM projection to the support-polygon boundary, and must remain positive.Source: §4.3 · pp. 5–6
5. Designing LEGO Walkers
The design problem is formulated as an optimization over leg geometry, layout, and actuation, with spatial requirements handled mechanically and temporal requirements through control. A three-stage solver first designs leg geometry and layout, then optimizes actuation.
5.1. Optimization Formulation
- The optimization searches leg-mechanism parameters, each leg’s placement, actuation controls, and support-phase start and end times.Actuation controls determine the foot locus’s temporal aspect; the other parameters determine its spatial shape.Source: §5.1 · p. 6
- The objective is a fabricable walker with a stable gait that approximates the target foot trajectory and maximizes the minimum stability margin.Gait approximation minimizes discrete Fréchet distance; the passage also identifies fabricability and stable walking as design objectives.Source: §5.1 · p. 6
- Constraints cover stable gait, singularity-free and collision-free motion, ground contact, duty factor, constant support-phase velocity, foot clearance, and fabricable gear profiles.Gear transmission ratios must remain within a reasonable range for smooth motion.Source: §5.1 · p. 6
5.2. Optimization Solver
- The three-stage solver designs leg geometry and layout for spatial targets, then optimizes leg actuation for temporal targets.Spatial objectives and constraints depend on foot-locus geometry; spatio-temporal constraints depend jointly on mechanism design and actuation.Source: §5.2 · p. 7
6. Results
The results show that the proposed mechanism more closely matches target foot paths than circular-gear and Jansen-linkage alternatives, while enabling varied walker designs. Simulations and fabricated prototypes demonstrate trajectory fidelity and coordinated locomotion.
Virtual results
- The approach designs walkers with varied leg counts and layouts, target foot trajectories, and body frames.Figure 8 marks the target trajectory in yellow and actual leg trajectories in green; its panels vary these design dimensions separately.Source: §6 · p. 7, Figure 8 · p. 8
Comparison with a LEGO-discretized Jansen linkage
- The designed mechanism closely matches the Jansen linkage’s foot trajectory with 10 link parts, 8 pins, and 76L total beam length.The LEGO-discretized Jansen linkage uses 14 link parts, 14 pins, and 134L total beam length.Source: §6 · p. 7, Figure 9 · p. 8
Evaluating the leg mechanism
- The tracked prototype trajectory closely aligns with simulation despite modeling simplifications in LEGO joints and tolerances.The simulated path has distinct support and transfer phases, with flat, stable ground-contact segments.Source: §6 · p. 8, Figure 12 · p. 9
Comparison with Coros et al.
- 0.073 versus 0.255 normalized Fréchet distance: the non-circular-gear mechanism matches a target curve more closely than Coros et al.’s circular-gear mechanism.The comparison attributes the difference to continuous pitch-curve design freedom from non-circular gears, versus a single gear ratio for circular gears.Source: §6 · p. 7, Figure 10 · p. 8
Physical fabrications
- Fabricated hexapod and quadruped walkers achieve coordinated leg motions and continuous forward locomotion; peak angular acceleration is 149.1°/s².The examples include a hexapod on uneven terrain and a quadruped on flat terrain.Source: §6 · pp. 8–9, Figure 11 · p. 9
7. Conclusion
The paper presents a computational approach that decouples leg-trajectory and timing control to design LEGO walkers with varied gaits and stable locomotion. Two walkers were fabricated and demonstrated in the real world; the current approach remains limited to statically stable creeping gaits and shared leg mechanisms.
7. Conclusion
- The approach co-designs morphology and control to produce LEGO walkers with varied walking gaits and stable locomotion.It decouples trajectory and timing control of the legs.Source: §7 · p. 9
- Two designed walkers were fabricated and demonstrated stable locomotion and walking gaits in the real world.Source: §7 · p. 9
- The current approach is limited to statically stable creeping gaits; avoiding expensive sensors and complex locomotion control restricts the achievable gait range.Source: §7 · p. 9
- The legs currently share the same mechanism design, while allowing different mechanisms could enrich gait diversity.Source: §7 · p. 10