Legged robots have demonstrated remarkable agility on rigid, stationary ground, but their locomotion reliability remains limited in non-inertial environments, where the supporting ground moves, tilts, or accelerates. Such conditions arise in ground transportation, maritime platforms, and aerospace settings, and they introduce persistent time-varying disturbances that break the stationary-ground assumptions underlying conventional legged locomotion. This survey reviews the state of the art in modeling, state estimation, and control for legged robots in non-inertial environments. We summarize representative application domains and motion characteristics, analyze the root causes of locomotion performance degradation, and review existing methods together with their key assumptions and limitations. We further identify open problems in robot-environment coupling, observability, robustness, and experimental validation, and discuss future directions in autonomy, system-level design, bio-inspired strategies, safety, and testing. The survey aims to clarify the technical foundations of this emerging area and support the development of reliable legged robots for real-world dynamic environments.
Robust and accurate proprioceptive state estimation of the main body is crucial for legged robots to execute tasks in extreme environments where exteroceptive sensors, such as LiDARs and cameras, may become unreliable. In this paper, we propose DogLegs, a state estimation system for legged robots that fuses the measurements from a body-mounted inertial measurement unit (Body-IMU), joint encoders, and multiple leg-mounted IMUs (Leg-IMU) using an extended Kalman filter (EKF). The filter system contains the error states of all IMU frames. The Leg-IMUs are used to detect foot contact, thereby providing zero-velocity measurements to update the state of the Leg-IMU frames. Additionally, we compute the relative position constraints between the Body-IMU and Leg-IMUs by the leg kinematics and use them to update the main body state and reduce the error drift of the individual IMU frames. Field experimental results have shown that our proposed DogLegs system achieves better state estimation accuracy compared to the traditional leg odometry method (using only Body-IMU and joint encoders) across various terrains. We make our code and datasets publicly available to benefit the research community (https://github.com/YibinWu/DogLegs).
Humanoid and quadrupedal robots have the potential to revolutionize the way we work, interact, and coexist with intelligent machines. To understand their effects on society and how they can enable scientific discovery, we assess the current capabilities of these systems along hardware, locomotion, autonomy, data, and applications. We identify recent advances and key open challenges that must be overcome to enable widespread adoption and new use cases for legged robots. Last, we provide an outlook on the future of legged robots, exploring their ethical considerations, economic potential, policy implications, and broader societal effects.
Legged robots carry an IMU, but the inertial solution drifts because consumer-grade IMUs are noisy. However, the feet create intermittent contacts with the environment that can be used to mitigate that drift. This report develops a sequence of increasingly expressive legged robot state estimators that leverage this. In all cases, the floating-base state comprises attitude, position, velocity, and IMU biases. To model foot contacts, we start from the contact-aided invariant EKF of Hartley et al., albeit at a reduced contact update rate. This is then augmented by replacing the measurement update by a small factor graph. Finally, we turn the same factors into a fixed-lag smoother with contact-episode footholds, with and without an evolving IMU bias. To facilitate reproducibility and further research in proprioceptive legged odometry, all four variants are available in GTSAM (Dellaert et. al), and we additionally provide a ROS2-compatible implementation.