cs.ROOct 5, 2026

RACER: Residual-Adaptive Closed-Loop Estimation for Sampling-Based Planning in Wheeled-Quadruped Racing

Authors: Yuxiang Liu, Marla Eisman, Lizhi Yang, Aaron Ames, Francesco Borrelli

Organizations: University of California, Berkeley, CA, USA. · California Institute of Technology, Pasadena, CA, USA.

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Abstract

We present RACER, a hierarchical control framework for wheel-based quadruped racing that combines an MPPI planner with a learned residual dynamics model and a low-level RL velocity tracker. The planner augments a nominal unicycle kinematic model with a neural residual term to capture the closed-loop tracking behavior of the RL policy. To train this residual model under limited real-world data, we propose Low-Rank Residual Adaptation (LoRRA), a two-stage approach that pre-trains on large-scale simulation data for broad coverage and then fine-tunes on a small real-world dataset with a low-rank constraint. In simulation, we empirically validate our engineering choices by showing (A) Residual dynamics improve the overall performance of our pipeline by capturing the tracking error of RL velocity tracker at high-speed cornering. (B) Residual dynamics trained with both source-domain and target-domain data gives racing performance significantly better than the residual dynamics trained with only target-domain data. (C) Low-rank constraint at target-domain adaptation gives higher success rates and higher performance than full-tune and from-scratch when domain gap in ground coefficient or joint gain increases.

Figures & tables

Fig. 1 : A Go2W Wheeled Quadruped racing along L-shape track using RACER framework. The low-level controller is a velocity RL-tracking policy; the high level planner is a DIAL-MPC controller equipped with residual dynamics trained with LoRRA.
Fig. 2 : System overview. An DIAL-MPC planner samples velocity commands at 10 Hz and rolls them out under f=funi+gϕ∗f=f_{\mathrm{uni}}+g_{\phi^{*}} . An RL tracker realises the chosen command at 50 Hz, producing 16-D joint targets for the Go2-W’s 12 leg joints and 4 wheel motors. Hardware adaptation refines only gϕ∗g_{\phi^{*}} to compensate domain shift, leaving the planner and tracker untouched.
Fig. 3 : The Source-Domain loss of residual dynamics L(ϕ,Ds)\mathcal{L}(\phi,\mathcal{D}_{s}) through the training with target-domain data Dt\mathcal{D}_{t} . See Sec. IV-B for definition of each training recipe: LoRRA, Full Tune, and From Scratch. Source and target environments are defined to be two simulation dynamics with different tire frictions, ∣μ∣=0.4|\mu|=0.4 . See Sec. IV-B1 for more details about domain definition. LoRRA(dual-phase training with low-rank constraint) helps preserve the most source-domain posterior with lowest source-domain loss after target-domain adaptation.
Fig. 4 : Simulation performance of Naive Unicycle (Blue) and RACER (Red) v.s. Capped velocity. RACER has stable performances independent of the velocity cap while the performance of naive unicycle is downgraded as the cap becomes higher. Horizontal axis: cap velocity. Vertical Axis: the performance metrics. See Sec. IV-A for the definition of naive unicycle. See Sec. IV-A1 for interpretations.
Fig. 5 : Residual Magnitude under different linear velocities(horizontal axis) and yaw rate changes(vertical axis). Residual magnitude positively correlates with linear velocities and yaw rate changes. Left: Residual of linear velocity; Right: residual of angular velocity. The brighter the area, the larger the residual.
Fig. 6 : Next-State Prediction Errors of RACER(left) and Naive Unicycle(right). Naive Unicycle’s prediction errors explode while cornering while RACER keeps the next-state prediction errors consistenly low. Heat Bar: next-state prediction errors. The brighter the points, the larger the prediction errors. Left: ∥st+1−(funi(st)+gϕ(st))∥\|s_{t+1}-(f_{\text{uni}}(s_{t})+g_{\phi}(s_{t}))\| . Right: ∥st+1−funi(st)∥\|s_{t+1}-f_{\text{uni}}(s_{t})\| . The trajectories of left are collected using RACER; The trajectories of right are collected using naive unicycle. A cross dot represents a lap failure.
velocity capMethodClean lapsAvg. vel.Max dev.
(m/s)(of 3)(m/s)(m)
1.5RACER3.0±0.0\mathbf{3.0\pm 0.0}1.21±0.011.21\pm 0.010.42±0.13\mathbf{0.42\pm 0.13}
Naive Unicycle2.3±1.22.3\pm 1.21.49±0.04\mathbf{1.49\pm 0.04}0.59±0.120.59\pm 0.12
2.0RACER3.0±0.0\mathbf{3.0\pm 0.0}1.41±0.02\mathbf{1.41\pm 0.02}0.45±0.08\mathbf{0.45\pm 0.08}
Naive Unicycle0.0±0.00.0\pm 0.00.000.000.83±0.570.83\pm 0.57
3.2RACER3.0±0.0\mathbf{3.0\pm 0.0}1.95±0.04\mathbf{1.95\pm 0.04}0.35±0.03\mathbf{0.35\pm 0.03}
TABLE I : Hardware counterpart of Fig. 4 . Racing metrics (mean ±\pm std over three runs) on the physical robot at different velocity caps vxv_{x} . RACER completes every lap and scales its speed as the caps become higher, whereas the naive unicycle finishes laps only at the conservative 1.51.5 m/s cap and fails entirely ( 00 laps) at higher speeds. Clean laps are out of 33 per run; bold marks the better value per metric.
Fig. 7 : Performance(Vertical Axis) of RACER using residual dynamics trained with LoRRA(blue), From Scratch(Yellow), Full-Tune(Green) under various domain gaps in terms of friction coefficient(horizontal Axis). The larger the domain gaps, the greater the advantages hold by LoRRA. Shaded Area: variance across seeds. For the definition of each training recipe, see Sec. IV-B
Fig. 8 : The advantage of LoRRA at preserving source-domain posterior increases with domain gap magnitude. The horizontal axis shows the domain gap Δμ\Delta\mu . The vertical axis shows the difference in source-domain loss after adapting residual dynamics to Dt\mathcal{D}_{t} , comparing Full-Tune against LoRRA: L(ϕ,Ds)Full-Tune−L(ϕ,Ds)LoRRA\mathcal{L}(\phi,\mathcal{D}_{s})_{\text{Full-Tune}}-\mathcal{L}(\phi,\mathcal{D}_{s})_{\text{LoRRA}} .
Fig. 9 : Hardware ablation experiments for RACER and LoRRA.
Fig. 10 : LoRRA gives performance consistently greater than or equal to From Scratch and Full Tune under different joint-gain domain gaps . This figure is the counterpart of Fig. 7 with domain gaps redefined as joint gain difference instead of friction difference.
ΔKp\Delta K_{p}MethodClean lapsAvg. vel.
(gap)(max is 3)(m/s)
0LoRRA3.00±0.00\mathbf{3.00\pm 0.00}1.94±0.071.94\pm 0.07
Full-Tune2.67±0.472.67\pm 0.472.06±0.05\mathbf{2.06\pm 0.05}
From-Scratch0.33±0.470.33\pm 0.470.59±0.830.59\pm 0.83
30LoRRA2.33±0.94\mathbf{2.33\pm 0.94}1.61±0.08\mathbf{1.61\pm 0.08}
Full-Tune1.00±0.821.00\pm 0.820.60±0.440.60\pm 0.44
TABLE II : Hardware LoRRA ablation (counterpart of Fig. 10 ). Racing metrics (mean ±\pm std over three independently trained seeds) for the three residual-training recipes under an increasing joint-gain domain gap ΔKp=∣Kp,s−Kp,t∣\Delta K_{p}=|K_{p,s}-K_{p,t}| (larger ΔKp\Delta K_{p} == larger gap; the residual is pre-trained at the nominal gain Kp,s=70K_{p,s}=70 ). LoRRA completes laps robustly across all gaps, whereas Full-Tune degrades as the gap grows and fails entirely at ΔKp=50\Delta K_{p}=50 , and From-Scratch fails at nearly every gap. Velocity is averaged over all seeds (a failed run contributes 00 velocity); bold marks the best value per metric.

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