Unknown payloads alter robot dynamics and make precise contact execution difficult when foothold margins are small. We present LOAD, a perceptive locomotion framework that combines explicit inertial estimates with implicit dynamics features for narrow-beam traversal. Separate recurrent modules infer torso inertial changes and task-relevant history from proprioception, while a height-map teacher is distilled into a depth-based student. We extensively evaluate LOAD and its variants in simulation and on hardware across beam widths and payload configurations. The results show that implicit dynamics features accelerate training, while explicit inertial estimation further improves traversal success; combining both enables LOAD to approach the performance of a privileged policy supplied with ground-truth inertial parameters. Hardware experiments demonstrate traversal with unilateral payloads of 6 kg on a 10 cm beam and 9 kg on a 15 cm beam, and an evenly distributed 11 kg payload on a 15 cm beam. These results support combining physical estimates and history features for precision locomotion under unknown loads.
Figures & tables
Fig. 1 : Overview of LOAD. Terrain perception, implicit dynamics features, and explicit inertial estimates jointly guide narrow-beam traversal under unknown payloads.
Fig. 2 : Overview of LOAD. sg denotes stop-gradient.
Reward term
Weight
Reward term
Weight
Linear velocity tracking
1
Soft joint limits
−10
Angular velocity tracking
1
Action rate
−0.05
Gait contact agreement
0.5
Joint acceleration
−2.5×10−7
Support-width posture
1
Foot clearance
−1
Standing posture
−1
Foot slip
−0.25
Upright orientation
−1
Touchdown impact
−10−3
TABLE I : Rewards used for training teacher policy.
Parameter
Range / value
Payload item count
{0,…,8}
Foot friction coefficient
[0.3,1.6]
Encoder bias (rad)
[−0.02,0.02]
Action delay (ms)
{0,5,10}
Proprio. noise bounds
±(0.20,0.05,0.01,1.50)
Height map noise (m) T
[−0.10,0.10]
TABLE II : Key domain randomization settings.
Inertial input
Implicit feature
None
Estimated
Ground truth
No
Baseline
Explicit
Explicit -GT
Yes
Implicit
LOAD
LOAD-GT
TABLE III : Policy variants by implicit feature and inertial input.
Fig. 3 : Teacher-policy comparison: (a) success rate over the latest 1,000 episodes on the narrowest beam (0.08 m). Faint lines show raw rates; bold lines show exponential moving averages with a 3 min time constant. (b) Varying beam width at 8 kg and (c) varying payload mass at 8 cm after 17,000 training iterations with left-side payloads. Shading in (b,c) shows pointwise 95% Wilson intervals over 192 trials (64 per evaluation seed); the vertical dashed line in (c) marks the 8 kg training limit.
Fig. 4 : Identification with a 6 kg left-side payload over 1024 episodes. Solid curves and bands show the mean and ±1 standard deviation; dashed lines indicate ground truth. The CoM panel and insets show the first second.
Fig. 5 : Full-episode mean absolute error (MAE) for random payloads: 0–8 kg within the training range and 9–12 kg outside it. Errors include the initial transient and give equal weight to each episode within a group.
Fig. 6 : Post-distillation traversal success of depth-based student policies with left-side payloads: (a) Explicit , (b) Implicit , and (c) LOAD. Each cell reports success (%) over 128 trials across four evaluation seeds. Dashed orange curves indicate interpolated 50% success contours.
Fig. 7 : Hardware demonstrations of LOAD on Go2 robot: (a) a 6 kg right-side payload on a 10 cm beam, (b) a 9 kg left-side payload on a 15 cm beam, and (c) an evenly distributed 11 kg payload on a 15 cm beam. Note that the payload masses exclude the 0.76 kg basket, and the beams have round edges with ∼ 1cm radius which reduces actual support width.
Fig. 8 : Beam traversal with a 6 kg right-side payload on a 0.15 m-wide beam: (a) foot placement, base trajectory, and estimated lateral velocity; (b) estimated and commanded forward velocities. Base and foot positions are reconstructed using a revised version of PRIME [ 31 ] that operates without motion-capture input.
Quadruped robots are increasingly expected to carry objects while moving through human environments. But what happens when a person interacts directly with the payload rather than with the robot? If the payload is unrestrained, the robot must distinguish intentional external interactions from ordinary payload motion, while still keeping the load balanced and maintaining stable locomotion. How can a quadruped infer and compliantly respond to such interactions using only onboard measurements? In this work, we develop a force-aware locomotion framework that treats payload interactions as commands that shape the motion of the combined robot-payload system. Our approach separates the learning of force-aware locomotion and force estimation on an unrestrained payload. We combine a compliant load-carrying policy with a causal force estimator, trained through estimator-in-the-loop data aggregation and finetuning, to predict interactions from onboard robot measurements. Our simulations and real-world experiments show that the resulting controller can maintain stable payload-carrying locomotion, yield compliantly to external interactions, and use the inferred force to support human-guided changes in the robot's trajectory.
Shaunak A. Mehta, Mayank Mishra, Prajit KrisshnaKumar +2
Fujitsu Research of America, Pittsburgh, PA, 15213.
Payload forces must be accommodated during locomotion, while leash forces can specify desired motion. We investigate whether a shared three-dimensional force estimate in newtons, inferred from proprioceptive history under sustained loading, can support both tasks. An estimator and locomotion policy are jointly trained with supervised force and velocity outputs and learned latent context. The estimated force conditions locomotion and additionally generates planar-velocity and yaw-rate commands for leash guidance through an analytical map. In sustained-force simulation sweeps, temporal means of componentwise force root mean square error range from 1.44 to 2.83,N. Compared with a domain-randomized baseline, the framework reduces velocity-tracking and base-orientation error scores by 21.6% and 46.5%, respectively, and increases mean survival from 68.29% to 94.60% in separate sustained-force tests. Unitree Go1 experiments demonstrate stationary vertical and horizontal force estimation, locomotion with an 8.5,kg payload whose weight exceeds the 70,N training force limit, and leash guidance using the same force-estimation interface.
Run Wang, Xu Yang, Alapati Tuerxun +1
Department of Automation, Tsinghua University, Beijing, China
Humanoid robots deployed in industrial environments are required to perform load-carrying transportation tasks that tightly couple locomotion and manipulation. However, achieving stable and robust locomotion under varying payloads and upper-body motions is challenging due to dynamic coupling and partial observability. This paper presents a load-aware locomotion framework for industrial humanoids based on a decoupled yet coordinated loco-manipulation architecture. Lower-body locomotion is controlled via a reinforcement learning policy producing residual joint actions on kinematically derived nominal configurations. A kinematics-based locomotion reference with a height-conditioned joint-space offset guides learning, while a history-based state estimator infers base linear velocity and height and encodes residual load- and manipulation-induced disturbances in a compact latent representation. The framework is trained entirely in simulation and deployed on a full-size humanoid robot without fine-tuning. Simulation and real-world experiments demonstrate faster training, accurate height tracking, and stable loco-manipulation. Project page: https://lequn-f.github.io/LALO/
Lequn Fu, Yijun Zhong, Xiao Li +4
Huazhong University of Science and Technology, Wuhan 430074, China · Beijing Humanoid Robot Innovation Center, Beijing 100086, China