Learning Keypoint Constraints from Visual Demonstrations for Safe Motion Planning

Learning from demonstrations (LfD) provides a framework for inferring unknown constraints from locally optimal, constraint-satisfying expert behavior. Existing approaches largely fall into two paradigms, constrained inverse optimal control (CIOC) and inverse constrained reinforcement learning (ICRL). CIOC exploits optimality conditions such as the Karush--Kuhn--Tucker (KKT) conditions but typically assumes known dynamics and structured constraint representations. Meanwhile, ICRL accommodates complex unknown constraints and unknown transition dynamics but often requires extensive online exploration, during which unsafe constraint violations may occur. In this work, we introduce Counterfactual KKT (CF-KKT), a constraint learning framework that leverages learned dynamics and locally optimal demonstrations to recover unknown constraints without requiring known dynamics or additional risky exploration, thereby combining the data efficiency and safety advantages of CIOC with the flexibility of ICRL. First, we use a locally learned differentiable dynamics model to impose KKT-inspired optimality conditions directly on the demonstrations. Second, we use the learned dynamics to generate reward-improving counterfactual behaviors near the demonstrations, revealing behaviors that would be preferable in the absence of the unknown constraint and thus providing synthetic infeasible data. When the constraint parameterization is known, the same learned-dynamics framework enables direct CIOC-based parameter recovery, and we characterize its sensitivity to dynamics misspecification. Across high-dimensional robotic control tasks, our approach learns neural constraint representations with improved safety and data efficiency relative to state-of-the-art offline ICRL baselines.

Generalization in robotic manipulation requires policies to perform tasks across diverse unseen object instances that vary in shape, size, and pose. However, conventional behavior cloning (BC) methods often overfit to instance-specific geometry and appearance, limiting transfer to novel objects. We introduce KeyGen, a framework that learns canonicalized semantic 3D keypoints from point clouds and uses them as structured object-centric representations for policy learning. A visuomotor diffusion policy conditions on these keypoints together with object-centric geometry to predict full manipulation trajectories, enabling consistent geometric correspondence across object instances. To evaluate category-level generalization, we construct a photorealistic simulation benchmark with three manipulation tasks and a planning-driven data generation pipeline that produces expert trajectories across diverse object instances. Experiments show that KeyGen significantly outperforms prior methods on both seen and unseen objects under pose variation, scales effectively with additional demonstrations per object, maintains robustness to object rescaling, and achieves strong performance in both simulation and real-world manipulation.

Vision-based manipulation policies are commonly learned from rich visual observations, typically using dense visual features extracted from full resolution images. It remains unclear how much of this visual information is really needed for effective policy learning. In this paper, we investigate the opposite end of the spectrum: how effective can manipulation policies be if they use as input only a compact visual representation. Sparse 2D keypoints provide a deliberately compact representation, giving the policy spatial information while removing direct access to appearance, texture, and background. We design AFFORD2ACT (Affordance-Guided Keypoints to Act) to study how much manipulation capability can be retained under this representation constraint. An off-the-shelf language-conditioned affordance model identifies the task-relevant region, from which up to 15 object keypoints are selected, together with 4 end-effector keypoints. The policy input is therefore reduced to only 19 2D keypoints (38 coordinates). A lightweight gating further decides which keypoints to pay attention to during execution. Across six real-robot manipulation tasks, this compact state outperforms the evaluated RGB, RGB-D, and dense-affordance behavior cloning baselines, degrades less as the number of demonstrations is reduced, and achieves 82% average success in held-out settings. Replacing learned gating with uniform weights reduces success from 92% to 52%. At the same time, the representation depends on reliable affordance localization and keypoint tracking, and remains vulnerable to incorrect masks, occlusion, tracking drift, and distractors.