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
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
ψmax
Max yaw angle
[−0.6,0.6]
0.6
rad
ψthres
Yaw threshold (SWING→WAIT FALL)
(−ψmax,ψmax)
0.55
rad
ϕup
Max leg roll
[−1.0,0]
-0.1
rad
ϕup_thres
Roll threshold (RISE→READY)
[−1.0,ϕup)
-0.15
rad
ϕdown
Min leg roll
[−1.0,ϕup_thres)
-1.0
rad
Δϕ
Touchdown offset
[0,ϕdown)
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 ⋅ m
TABLE II: Simulated robot properties
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
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.
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
Multi-legged elongate robots hold promise for maneuvering through complex environments. Prior work has demonstrated that reliable locomotion can be achieved using open-loop body undulation and foot placement on rugose terrain. However, robust navigation through confined spaces remains challenging when body-environment contact is extensive and terrain rheology varies rapidly. To address this challenge, we develop a pair of tactile antennae for multi-legged robots that enable real-time sensing of surrounding geometry, modeling the morphology and function of biological centipede antennae. Each antenna features gradient compliance, with a stiff base and soft tip, allowing repeated deformation and elastic recovery. Robophysical experiments reveal a relationship between continuous antenna curvature and contact force, leading to a simplified mapping from antenna deformation to inferred discrete collision states. We incorporate this mapping into a controller that selects among a set of locomotor maneuvers based on the inferred collision state. Experiments in obstacle-rich and confined environments demonstrate that tactile feedback enables reliable steering and allows the robot to recover from near-stuck conditions without requiring global environmental information or real-time vision. These results highlight how mechanically tuned tactile appendages can simplify sensing and enhance autonomy in elongate multi-legged robots operating in constrained spaces.
Zhaochen J. Xu, Juntao He, Delfin Aydan +5
All authors are with the Georgia Institute of Technology, Atlanta, GA 30332, USA.
Enabling robots to walk on yielding terrain is vital for applications ranging from disaster response to planetary exploration. While bipedal robots hold immense potential, their locomotion on deformable surfaces remains limited as current simulators fail to capture the spatiotemporal heterogeneity of such yielding substrates. We present MILD, featuring a physics-grounded discrete-element contact solver that accurately simulates spatially varying foot-terrain interactions. Complementing this model, we train a terrain-aware locomotion controller via deep reinforcement learning with latent modulation and proprioceptive estimation. Quantitative comparisons against state-of-the-art methods show our approach generates more diverse and realistic contact scenarios during training, resulting in controllers that exhibit natural adaptation on real deformable surfaces. Through hardware experiments, we demonstrate the system's capability for online terrain identification and adaptation across a wide range of surface stiffness.
Zeren Luo, Jiahui Zhang, Zhe Xu +6
Adaptive Robotic Controls Lab (ArcLab), Department of Mechanical Engineering, The University of Hong Kong, Hong Kong · School of Mechanical and Electrical Engineering, Beijing Institute of Technology, Beijing, China · Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan