cs.ROOct 13, 2026

Locomotion with Online Awareness of Dynamics for Precision Footholds

Authors: Kunzhao Ren, Zhishuo Zhu, Xiaobin Xiong

Organizations: Shanghai Innovation Institute. · University of Wisconsin-Madison.

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Abstract

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 termWeightReward termWeight
Linear velocity tracking11Soft joint limits−10-10
Angular velocity tracking11Action rate−0.05-0.05
Gait contact agreement0.50.5Joint acceleration−2.5×10−7-2.5\times 10^{-7}
Support-width posture11Foot clearance−1-1
Standing posture−1-1Foot slip−0.25-0.25
Upright orientation−1-1Touchdown impact−10−3-10^{-3}
TABLE I : Rewards used for training teacher policy.
ParameterRange / value
Payload item count{0,…,8}\{0,\ldots,8\}
Foot friction coefficient[0.3,1.6][0.3,1.6]
Encoder bias (rad)[−0.02,0.02][-0.02,0.02]
Action delay (ms){0,5,10}\{0,5,10\}
Proprio. noise bounds±(0.20,0.05,0.01,1.50)\pm(0.20,0.05,0.01,1.50)
Height map noise (m) T[−0.10,0.10][-0.10,0.10]
TABLE II : Key domain randomization settings.
 Inertial input
Implicit featureNoneEstimatedGround truth
NoBaselineExplicitExplicit -GT
YesImplicitLOADLOAD-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\pm 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 ∼\sim 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.
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