Walking on Rough Terrain with Any Number of Legs

Zhuoyang Chen; Xinyuan Wang; Shai Revzen

cs.ROMar 10, 2026

Walking on Rough Terrain with Any Number of Legs

Authors: Zhuoyang Chen, Xinyuan Wang, Shai Revzen

Organizations: The authors are with the University of Michigan, Ann Arbor, MI 48109, USA.

Abstract

Robotics would gain by replicating the remarkable agility of arthropods in navigating complex environments. Here we consider the control of multi-legged systems which have 6 or more legs. Current multi-legged control strategies in robots include large black-box machine learning models, Central Pattern Generator (CPG) networks, and open-loop feed-forward control with stability arising from mechanics. Here we present a multi-legged control architecture for rough terrain using a segmental robot with 3 actuators for every 2 legs, which we validated in simulation for robots with 6 to 16 legs. Segments have identical state machines, and each segment also receives input from the segment in front of it. Our design bridges the gap between WalkNet-like event cascade controllers and CPG-based controllers: it tightly couples to the ground when contact is present, but produces fictive locomotion when ground contact is missing. The approach may be useful as an adaptive and computationally lightweight controller for multi-legged robots, and as a baseline capability for scaffolding the learning of machine learning controllers.

Figures & tables

Panel of Figure 1 — Fig. 1: Modular mechanical design of the robot. A segment (left) has 3 DOF: two leg motors rotate about the x-axis, and a yaw motor rotates about the z-axis. This modular design can be chained with backbone joints to create a hexapod (middle), or, e.g. a decapod (right). We build a hexapedal version (right, photo)

Fig. 2: State machine architecture used for hierarchical yaw-leg coordination.

Parameter	Description	Range	Value	Unit
$\psi_{max}$	Max yaw angle	$[-0.6,0.6]$	0.6	rad
$\psi_{thres}$	Yaw threshold (SWING→WAIT FALL)	$(-\psi_{max},\psi_{max})$	0.55	rad
$\phi_{up}$	Max leg roll	$[-1.0,0]$	-0.1	rad
$\phi_{up\_thres}$	Roll threshold (RISE→READY)	$[-1.0,\phi_{up})$	-0.15	rad
$\phi_{down}$	Min leg roll	$[-1.0,\phi_{up\_thres})$	-1.0	rad
$\Delta\phi$	Touchdown offset	$[0,\phi_{down})$	0.6	rad

TABLE I: Control Parameters

Fig. 3: The 3-segment hexapod robot simulated on a rough terrain in the MuJoCo simulator.

Part	Property	Value
All 3D-printed / laser-cut parts	PLA density	1.24 g/cm 3
Compliant parts	300 stainless steel density	8.0 g/cm 3
Dynamixel MX-64	Mass	126 g
	No-load speed	78 RPM
	Holding torque	7.3 N $\cdot$ m

TABLE II: Simulated robot properties

Panel of Figure 6 — Fig. 4: Robustness of Phase Convergence. The phase error decays rapidly on both ideal Flat Terrain (Blue) and Random Rough Terrain (Red Dashed). Despite the significant ground irregularities in the random terrain case, the distributed controller successfully synchronizes the legs, demonstrating that the gait stability is robust to environmental noise. This performance is consistent across both the (a) 6-legged and (b) 16-legged configurations.

Fig. 5: Body and foot trajectories, phase difference, and body posture convergence for a 3-segment robot simulated on (a) floating terrain, (b) flat terrain, (c) random terrain, (d) hill terrain, and (e) stair terrain. We omitted the body posture in the floating scene as it is not well defined

Fig. 6: Body and foot trajectories, phase difference, and body posture convergence for an 8-segment robot simulated on (a) floating terrain, (b) flat terrain, (c) random terrain, (d) hill terrain, and (e) stair terrain. We omitted the body posture in the floating scene as it is not well defined

Legged Robotics

Legged robotics studies how robots with legs move, perceive their surroundings, and perform useful tasks across varied terrain.

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Sep 27, 2026J/K move · Enter open · S save

Multi-Terrain Mastery: A Comprehensive Controller for Bipedal Locomotion

Oluwami Dosunmu-Ogunbi, Aayushi Shrivastava

Mechanical Engineering Department Ohio Northern University Ada, United States of America · Mechanical Engineering Department University of California, Berkeley Berkeley, United States of America

Robot Locomotion Legged Robotics Humanoid Robot Locomotion Terrain-Aware Robot Locomotion

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Advancing bipedal robots to navigate diverse terrains remains a significant challenge in robotics. Traditional locomotion controllers excel on specific surfaces but struggle across varied environments, limiting their practical applications. Given the unpredictable nature of real-world environments, a single controller capable of handling multiple terrains is ideal, eliminating the need for multiple specialized controllers. We propose a multi-terrain controller to enhance the versatility and robustness of bipedal locomotion. Building on previous work with a stance ankle motor for stability on inclined and rough surfaces, this paper extends capabilities to steep wet uneven grassy slopes, and compliant terrains such as sand, gravel, rocks, and constrained terrains like staircases. To address the unique demands of these terrains, we introduce a new impact map that is essential for maintaining performance and robustness against unseen terrains. We also discuss in detail the control structure for real-time deployment on the robot. We validate our controller on the 20 degree-of-freedom Cassie bipedal robot.

Abstract

Legged Robotics

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