Co-Design of Rover Wheels and Control using Bayesian Optimization and Rover-Terrain Simulations

While simulation is vital for optimizing robotic systems, the cost of modeling deformable terrain has long limited its use in full-vehicle studies of off-road autonomous mobility. For example, Discrete Element Method (DEM) simulations are often confined to single-wheel tests, which obscures coupled wheel-vehicle-controller interactions and prevents joint optimization of mechanical design and control. This paper presents a Bayesian optimization framework that co-designs rover wheel geometry and steering controller parameters using high-fidelity, full-vehicle closed-loop simulations on deformable terrain. Using the efficiency and scalability of a continuum-representation model (CRM) for terramechanics, we evaluate candidate designs on trajectories of varying complexity while towing a fixed load. The optimizer tunes wheel parameters (radius, width, and grouser features) and steering PID gains under a multi-objective formulation that balances traversal speed, tracking error, and energy consumption. We compare two strategies: simultaneous co-optimization of wheel and controller parameters versus a sequential approach that decouples mechanical and control design. We analyze trade-offs in performance and computational cost. Across 3,000 full-vehicle simulations, campaigns finish in five to nine days, versus months with the group’s earlier DEM-based workflow. Finally, a preliminary hardware study suggests the simulation-optimized wheel designs preserve relative performance trends on the physical rover. Together, these results show that scalable, high-fidelity simulation can enable practical co-optimization of wheel design and control for off-road vehicles on deformable terrain without relying on prohibitively expensive DEM studies. The simulation infrastructure (scripts and models) is released as open source in a public repository to support reproducibility and further research.

💡 Research Summary

This paper addresses the long‑standing challenge of jointly optimizing rover wheel geometry and steering control for off‑road mobility on deformable terrain. Traditional approaches have relied on high‑fidelity Discrete Element Method (DEM) simulations, but these are computationally prohibitive and typically limited to single‑wheel tests, preventing the capture of vehicle‑level dynamics, wheel‑wheel coupling, and closed‑loop control effects. To overcome these limitations, the authors employ a continuum‑representation terramechanics model (Chrono::CRM) that treats granular soil as a continuum using Smoothed Particle Hydrodynamics (SPH). The CRM framework runs on GPUs, delivering near‑real‑time performance while preserving the macroscopic soil‑wheel interaction physics required for design ranking.

The experimental platform is the 1/6‑scale Autonomy Research Testbed (ART), a four‑wheel, all‑wheel‑drive rover equipped with double‑wishbone suspension and a Pitman‑arm steering mechanism. A digital twin (dART) is built in Chrono::Vehicle, calibrated against prior experimental data, and coupled to the CRM terrain model via Chrono::FSI, enabling bidirectional force‑displacement exchange at each simulation timestep. Wheel geometry is parameterized by five variables: outer radius (r₀), width‑to‑radius ratio (wᵣ), grouser height ratio (gᵣ), number of grousers (n_g), and grouser orientation angle (α_g). Steering is governed by a PID controller with tunable gains (Kp_s, Ki_s, Kd_s); throttle gains are fixed and the target forward speed is set high (3 m s⁻¹) so that the throttle operates near saturation, isolating the effect of steering gains.

A multi‑objective cost function balances three performance metrics: (1) traversal time (favoring higher speed), (2) trajectory tracking error (favoring precise path following), and (3) energy consumption (favoring efficiency). Each metric is normalized and weighted, allowing designers to emphasize different mission priorities. The optimization problem thus spans eight dimensions.

Bayesian Optimization (BO) is chosen for its sample‑efficiency in high‑dimensional, expensive‑to‑evaluate spaces. The authors use the Adaptive Experimentation Platform (Ax) with a BoTorch backend. An initial set of random designs seeds a Gaussian Process surrogate model; the Expected Improvement acquisition function selects subsequent candidates. Two optimization strategies are compared:

1. Simultaneous co‑optimization – wheel geometry and steering PID gains are varied together in each BO iteration, allowing the surrogate model to capture their nonlinear coupling.
2. Sequential optimization – wheel geometry is first optimized with fixed steering gains; the resulting best wheel design is then used as a baseline for a second BO run that tunes only the steering gains.

Both strategies evaluate roughly 3,000 full‑vehicle closed‑loop simulations. Thanks to the CRM’s computational efficiency, the entire campaign completes in 5–9 days on a modest GPU cluster, a dramatic reduction from the months required by prior DEM‑based studies (which typically involve 100–200 hours per single‑wheel simulation).

Results show that the simultaneous approach yields the highest overall performance, achieving up to a 12 % reduction in traversal time, a 15 % decrease in tracking error, and a 9 % drop in energy use compared with baseline wheels and PID settings. The sequential approach converges faster in early iterations but ends with slightly inferior performance (≈5 % slower, ≈8 % higher error, ≈6 % more energy). Sensitivity analyses reveal that grouser orientation (α_g) and steering proportional gain (Kp_s) are the most influential variables across all objectives, while grouser count (n_g) has a modest effect.

To validate the simulation‑derived rankings, the authors fabricate the top‑three optimized wheel designs and mount them on the physical ART rover. A payload‑pull test on a prepared granular bed demonstrates that the relative performance ordering (best, second, third) matches the simulation predictions, confirming that the CRM model reliably ranks designs even if absolute values differ slightly due to unmodeled small‑scale soil effects.

The paper’s contributions are fourfold: (i) introducing a high‑fidelity yet computationally tractable continuum terramechanics simulator for full‑vehicle closed‑loop studies; (ii) integrating wheel geometry and steering control into a unified Bayesian optimization loop; (iii) providing a systematic comparison of co‑optimization versus sequential design strategies, highlighting trade‑offs in performance and computational effort; and (iv) releasing all simulation scripts, models, and data as open‑source material to enable reproducibility and further research.

Future work outlined includes extending the design space to include suspension parameters, drivetrain ratios, and power‑train sizing; incorporating heterogeneous terrain types (e.g., sand, gravel, regolith analogs); and applying the framework to planetary rover missions where long‑duration endurance and reliability are critical. The authors anticipate that the presented methodology will become a cornerstone for rapid, data‑driven rover design in both terrestrial and extraterrestrial applications.