Learning Purposeful Co-designs of Bio-inspired Quadrupedal Robots

Fabio Boekel, Jiatao Ding, Cosimo Della Santina

November 2026

TL;DR Dogger is a 3D-printed quadruped whose leg segment lengths and knee springs can be swapped. One RL policy trained across all designs, combined with Bayesian optimization, picks a leg design for each task. Deployed zero-shot, the chosen designs cut cost of transport by 18.6% for inspection walking and 35.7% when carrying a 2 kg payload.

What they do

Co-design of legged robots often searches a narrow mechanical space, such as knee elasticity alone. Dogger is a 6.5 kg quadruped with three-segment legs and a parallel knee spring; link lengths and spring settings change by reprinting or swapping parts. A two-stage RL plus Bayesian optimization (BO) pipeline picks a leg design for each task, and the design and policy go to hardware without retraining.

How it works

Design space. Five parameters: three link-length scale factors (0.7-1.3), the spring wheel diameter (0-50 mm, sets knee stiffness) and the spring offset (0-10 mm, sets where the spring engages).
Universal policy. One PPO policy takes the design parameters as input and trains across randomly sampled designs in up to 8,192 parallel environments. Training takes 15 min to 2 h on an RTX 4070.
Design selection. With the policy frozen, BO (Optuna’s TPE solver) finds the design with the lowest cost of transport for the task. The energy model counts motor losses and the constant power draw of the electronics.
Sim-to-real. Domain randomization, observation noise, velocity disturbances and a feedforward torque for the knee spring. The policy runs at 50 Hz on a Jetson Orin Nano.

Results

Inspection walking: the selected design lowers cost of transport by 12.6% in simulation and 18.6% ± 1.7% on hardware, relative to the nominal design with springs disengaged. With a 2 kg payload: 34.0% in simulation, 35.7% ± 3.1% on hardware.
Each design also helps on the other task (13.5% and 23.7% on hardware), but less than the design selected for that task.
In simulation, link lengths alone give 1.1% (inspection) and 24.0% (payload) and springs alone give 7.3% and 16.3%. Optimizing both gives the largest gain on both tasks.
A CPG + CMA-ES co-design baseline is 4.0% better on inspection but 3.2% worse with the payload; privileged RL + BO is 12.8% and 3.7% worse. Outdoors, the robot walked on gravel, tall grass, soil and forest debris, and one continuous 17-minute trial ran without a fall.

Limitations

Designs are selected under a fixed, pretrained policy, so the chosen morphology depends on what that controller can do. Quantitative comparisons are on flat ground only, with two tasks and five design variables. About half the measured energy goes to the electronics, which no leg design can reduce.

Videos

Figures

From Figure 1: The bio-inspired three-segment leg. Link lengths are scaled from their nominal values, the spring whee... — From Figure 1: The bio-inspired three-segment leg. Link lengths are scaled from their nominal values, the spring wheel diameter sets the knee stiffness and the spring offset sets the angle where the spring engages. The middle inset shows the clamps that set the offset; the right panel shows three spring-wheel sizes.

From Figure 2: Two-stage co-design. Step 1 trains one universal RL policy across the design space in simulation; step... — From Figure 2: Two-stage co-design. Step 1 trains one universal RL policy across the design space in simulation; step 2 uses Bayesian optimization to pick the most energy-efficient design for a task. On hardware, a feedforward spring torque is added to the policy output to help bridge the sim-to-real gap.

From Figure 5: Design-space ablation in simulation. Change in cost of transport relative to the fixed nominal design ... — From Figure 5: Design-space ablation in simulation. Change in cost of transport relative to the fixed nominal design for task 1 (left) and task 2 (right), optimizing link lengths only (purple), springs only (green) or both (yellow); error bars show standard deviations.

From Figure 7: Two robot configurations walking on unstructured outdoor terrain; the one in the bottom two rows has a... — From Figure 7: Two robot configurations walking on unstructured outdoor terrain; the one in the bottom two rows has a longer shank.

Abstract

Treating morphology and control as separate design problems has constrained the efficiency and adaptability of quadrupedal robots, while current co-design approaches are often constrained by restricted design spaces. We overcome this limit by introducing Dogger, a bio-inspired quadruped with modular three-segment legs, four-bar linkages and adjustable passive knee compliance. A two-stage framework combining reinforcement learning and Bayesian optimization is developed: the morphology-conditioned control policy is trained across designs and then held fixed during task-specific design selection. The resulting designs and policies deployed zero-shot reduce the cost of transport by 18.6% and 35.7% for inspection and payload-carrying tasks. Comparisons demonstrate that full geometry-compliance co-design outperforms fixed and restricted design scopes. Cross-task tests further reveal distinct task-specific morphologies with shared mechanical trade-offs. These results provide hardware-level evidence that expanding the physical design space alongside learned control is essential to realize the full potential of task-driven morphology-control co-design in legged robotics.

Summaries are written automatically from each paper's text. Figures and videos come from the paper and its project page; all credit goes to the authors.

Matt Strong