Control co-design jointly optimizes a robot's physical design and its controller. Existing techniques are limited in the number of model parameters and the complexity of the physical models they can handle. In this paper, we propose a gradient-based bilevel formulation that replaces the dynamics models of earlier techniques with a differentiable neural surrogate and differentiates through the trajectory optimizer using a structure-exploiting approach. We validate the framework on fixed-wing gliders, using NeuralFoil as the aerodynamic surrogate. The tasks are maximum-distance gliding, minimum-distance landing, and perching. Experiments on 2D airfoils and 3D wings show that our method runs about five times faster than a state-of-the-art evolutionary baseline. It also outperforms pipelines that optimize aerodynamic proxy metrics.
Figures & tables
Fig. 1 : Co-design . We jointly optimize the airfoil shape (left, colored by iteration) and the controls. The shape determines the trajectories (right) through a neural surrogate, and the gradient flows back by implicit differentiation. Without the validity constraint (bottom), the optimizer drives the shape to where the surrogate is unreliable.
Fig. 2 : Overview. The neural surrogate is evaluated on the flight envelope once per design update and replaced by a polynomial, which the trajectory optimizations, one per task and launch state, use instead of the network. The design gradient and the validity constraint are detailed in Secs. III-B and III-C .
Fig. 3 : Glider model. (a) Dots mark the centers of mass. Lengths on the left are measured from O . (b) Model parameters.
Fig. 4 : Tasks and controls. Optimized airfoils (left), trajectories (middle), and mission cost over the outer iterations (right) for the three tasks, colored by run progress (dashed: initial design).
Method
Gliding
Landing
Perching
min
Initial design
− 24.3 ± 0.5
– (0/3)
– (2/3)
16
Seq. max L/D
− 40.8 ± 12.8
– (2/3)
– (1/3)
93
Seq. max CL,max
− 25.5 ± 4.9
– (2/3)
25.49 ± 14.79
83
Seq. max CD
− 37.3 ± 2.0
– (2/3)
– (2/3)
81
GA
− 33.0 ± 7.2
244 ± 7
8.63 ± 0.19
246
CMA-ES
− 39.3 ± 9.5
– (2/3)
9.13 ± 0.57
265
TABLE I : Comparison with the baselines. Mission cost Φ (lower is better), re-scored with XFoil. Mean ± std over I1–I3 if feasible on all three, else the number of feasible inits ( t/c≥0.05 , c≥0.6 at visited operating points). Bold : best; min: median wall-clock.
Fig. 5 : Pareto front between landing cost and glide distance. The line interpolates all the non-dominated designs among all those evaluated by the sweep. Gray represents dominated designs.
Fig. 6 : 3D wing, perching task. Time per design update versus number of design parameters. Only the time to compute the wing model grows. The insets show wings with 4 and 7 sections.
Fig. 7 : Time per design update versus surrogate size. Ours stays constant; with the network inside the OCP or the simultaneous NLP, the cost grows.
Fig. 8 : Without the confidence constraint, the optimizer exploits the model. Short landing. Left: model cost and mean confidence per iteration. Right: model error against XFoil for each final design (gray: XFoil fails; blue: flights). Bottom: final airfoils.
Co-design optimisation of autonomous systems has emerged as a powerful alternative to sequential approaches by jointly optimising physical design and control strategies. However, existing frameworks often neglect the robustness required for autonomous systems navigating unstructured, real-world environments. For agile Unmanned Aerial Vehicles (UAVs) operating at the edge of the flight envelope, this lack of robustness yields designs that are sensitive to perturbations and model mismatch. To address this, we propose a robust co-design framework for agile fixed-wing UAVs that integrates parametric uncertainty and wind disturbances directly into the concurrent optimisation process. Our bi-level approach optimises physical design in a high-level loop while discovering nominal solutions via a constrained trajectory planner and evaluating performance across a stochastic Monte Carlo ensemble using feedback LQR control. Validated across three agile flight missions, our strategy consistently outperforms deterministic baselines. The results demonstrate that our robust co-design strategy inherently tailors aerodynamic features, such as wing placement and aspect ratio, to achieve an optimal trade-off between mission performance and disturbance rejection.
Adrian Andrei Buda, Xavier Chen, Nicolò Botteghi +1
Department of Aeronautics, Imperial College London, United Kingdom · Department of Mathematics, Politecnico di Milano, Italy
Replicating and surpassing the autonomy of natural organisms remains a long-standing goal in robotics. Yet most robotic systems have their structure, materials, and control designed separately, in sharp contrast to the co-evolution in nature. This separation often leads to suboptimal designs, and we still have a limited understanding of the individual and collective contributions of these design entities. In this work, we propose a gradient-based co-design framework that simultaneously optimizes the topology, material distribution, and control policy of a truss-lattice robot. The framework embeds mixed-type topological and material variables into a continuous design space and integrates a neural network controller within a differentiable simulator, capturing their interactions and enabling efficient gradient calculation via automatic differentiation. Furthermore, we develop a constrained optimization to navigate the highly non-convex design landscape and jointly optimize all design entities. Case studies demonstrate that the proposed framework consistently discovers diverse locomotion strategies that outperform baselines obtained through separated design. The framework is also flexible to accommodate different functional requirements and boundary conditions. Using this framework, we further extract design insights that reveal the individual and collective effects of different entities on robotic performance. The proposed framework provides a computational foundation for the autonomous co-design of robotic systems, capable of reconfiguration, locomotion, and other complex autonomous behaviors.
Qinsong Guo, Liwei Wang
Dept. of Mechanical Engineering Carnegie Mellon University Pittsburgh, PA 15213
Co-design is a high-dimensional search problem in the robot morphology and control design space. Efficient search requires exploiting the structure shaped by their interaction. To understand this structure, we analyze the landscapes of soft locomotion and manipulation tasks. We identify three patterns consistent across regions of their co-design spaces: 1) Within a region, quality varies along a low-dimensional manifold, with minimal variation orthogonal to it, reducing the effective search space dimensionality. 2) In higher-quality regions, the variance in quality is spread across more dimensions, necessitating search to expand dimensionality as quality improves. 3) In higher-quality regions, quality varies along joint morphology-control dimensions, requiring search along them. Using these insights, we devise an efficient co-design algorithm that yields 36% better co-designs than state-of-the-art baselines. We examine their exploration patterns and show that these baselines required an order of magnitude more function evaluations to find co-designs of comparable quality. Finally, we ablate our algorithm to verify that exploiting the identified structure was the key to efficient co-design.
Apoorv Vaish, Oliver Brock
Robotics and Biology Laboratory, Technische Universität Berlin · Science of Intelligence (SCIoI), Cluster of Excellence, Berlin · Robotics Institute Germany (RIG)