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.
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Figure 2: Existing LEGO walkers [ 1 ] often rely on bulky and complex mechanisms, yet delivering only a fixed walking gait.
Figure 3: Illustration of our LEGO walker. Left: our leg mechanism comprises a five-bar linkage of LEGO Technic bricks together with a pair of non-circular gears. Right: each leg is attached to the main body and actuated by an independent motor.
Figure 4: Overview of our approach. (a) The input includes a main body with a plane for leg placement (in blue), a target foot trajectory, and a footfall pattern. (b) Our approach automatically designs a compatible leg mechanism and optimizes the placement of the legs and their actuation control. (c) Our approach also generates a LEGO-style assembly manual, providing instructions to aid the assembly of the walker. (d) Our fabricated LEGO walker can walk stably, following the target gait.
Figure 5: Our leg mechanism. (a) Our employed LEGO Technic bricks, each with a unique ID. The gray beams are the main links in our leg mechanism; the blue beams with axle holes are for connecting with gears; and the yellow pins are revolute joints for connecting the links while allowing relative motion between them. (b) The schematic of our leg mechanism, which is a five-bar linkage with a pair of non-circular gears. The rotation centers of the two gears are fixed relative to the body frame.
Figure 6: The foot locus of a leg mechanism. The foot locus is the trajectory traced by the foot over a single gait cycle, consisting of a support phase (in blue) and a transfer phase (in yellow and green). (a) The foot locus when the walker is stationary. (b) The foot locus when the walker is moving.
Figure 7: An illustration of the static stability condition. The red dot denotes the projection of the center of mass (COM) onto the ground plane, whereas the blue polygon represents the support polygon formed by the feet currently in contact with the ground (blue dots). The static stability margin is illustrated by the black dashed line.
Figure 8: Our approach allows designing a variety of LEGO walkers. For each result, the target foot trajectory is shown in yellow at the walker’s right front leg, while the actual foot trajectories are shown in green for all the legs. (a) We vary the number of legs and the leg layout, while fixing the body frame and the target foot trajectory. (b) We vary the target foot trajectory, while fixing the body frame and the number of legs. (c) We vary the body frame, while fixing the number of legs and the target foot trajectory.
Figure 9: Taking the foot trajectory of (left) the Jansen linkage as the target curve, (right) our designed leg mechanism generates a foot trajectory that closely matches the target. Compared with the Jansen linkag, our leg mechanism has fewer parts, a simpler mechanical structure, and a smaller size.
Figure 10: Given the same target curve (in red color), (right) our leg mechanism generates a curve that more closely matches the target curve than (left) that of Coros et al. [ 5 ] , due to the larger design space enabled by the non-circular gears.
Figure 11: Key frames of two LEGO walkers designed by our approach and fabricated using LEGO Technic and 3D printing. (Top) A hexapod LEGO walker without a body frame performs locomotion on uneven terrain. (Bottom) A quadruped LEGO walker with a Sci-Fi body frame performs locomotion on flat terrain. Please refer to the accompanying video for the full walking locomotion.
Figure 12: Evaluating the kinematic performance of a leg mechanism designed by our approach. (Left) Our designed leg mechanism, where the simulated foot trajectory is shown in green. (Right) Corresponding view of our LEGO-built prototype, where the actual foot trajectory is tracked on video images and visualized in orange.
Figure 13: Control sequence analysis on one of the leg mechanisms in our hexapod LEGO walker shown in Figure .