Co-design is powerful and not free

TL;DR

This work addresses when morphology–control co-design adds value beyond control-only optimization in embodied robots. It introduces a unified end-to-end framework that embeds morphology and control within a single neural policy and compares co-design to control-only under fair protocols, evaluating static-obstacle reaching with metrics such as trajectory error, final error, and collision penalties. The key contributions include a principled fairness scheme to separate controller capacity from morphological integration, empirical evidence that co-design improves performance primarily when geometry constrains the task, and practical guidelines to decide when to co-design versus optimize control alone. The findings offer actionable guidance for embodiment-aware robot design and lay the groundwork for benchmarks that systematically probe the necessity of co-design across tasks and environments.

Abstract

Robotic performance emerges from the coupling of body and controller, yet it remains unclear when morphology-control co-design is necessary. We present a unified framework that embeds morphology and control parameters within a single neural network, enabling end-to-end joint optimization. Through case studies in static-obstacle-constrained reaching, we evaluate trajectory error, success rate, and collision probability. The results show that co-design provides clear benefits when morphology is poorly matched to the task, such as near obstacles or workspace boundaries, where structural adaptation simplifies control. Conversely, when the baseline morphology already affords sufficient capability, control-only optimization often matches or exceeds co-design. By clarifying when control is enough and when it is not, this work advances the understanding of embodied intelligence and offers practical guidance for embodiment-aware robot design.

Figures (9)

• Figure 1: System Architecture Overview
• Figure 2: Task hierarchy categorized into static and dynamic tasks with increasing complexity
• Figure 3: Co-design accelerates convergence and reduces tracking error. (a) Co-design versus (b) control-only on the same reaching task with static obstacles, where the top row plots the best loss per generation and the bottom row shows the end-effector trajectory (blue) towards the target (red). Loss includes tracking error and a collision penalty; in this example the reported collisions are zero for both methods. Co-design converges within $\sim$20--30 generations to a lower plateau loss ($\approx 0.02$), whereas control-only requires $\sim$100 generations and plateaus higher ($\approx 0.03$), yielding a larger residual offset in the final trajectory.
• Figure 4: patial advantage of co-design across target locations and obstacle layouts. Each panel reports a $\Delta$-map over the target grid, with color encoding improvement at each target: for error-based metrics we use $\Delta = \text{err}_{\text{control}} - \text{err}_{\text{co}}$, and for success we use $\Delta = \text{succ}_{\text{co}} - \text{succ}_{\text{control}}$; thus red indicates co-design is better, and blue indicates control-only is better.
• Figure 5: Histogram of final position error across obstacle layouts. Each panel (a--e) compares the distribution of end-of-rollout error $\varepsilon_{\text{final}}$ (meters) for co-design (blue) and control-only (orange). Insets show the corresponding target grid and obstacle geometry (grey). Co-design concentrates more mass in the low-error regime (0--0.10 m) and suppresses large-error tails ($\ge$0.25 m) in most constrained layouts, whereas distributions largely overlap in open workspaces. A localized exception (panel c) shows a mild control-only advantage around 0.10--0.20 m, consistent with morphology--dynamics trade-offs for clearance.