DA-MMP: Learning Coordinated and Accurate Throwing with Dynamics-Aware Motion Manifold Primitives

TL;DR

This work proposes Dynamics-Aware Motion Manifold Primitives (DA-MMP), a motion generation framework for goal-conditioned dynamic manipulation, and instantiate it on a challenging real-world ring-tossing task and shows that it can generate coordinated and smooth motion trajectories for the ring-tossing task.

Abstract

Dynamic manipulation is a key capability for advancing robot performance, enabling skills such as tossing. While recent learning-based approaches have pushed the field forward, most methods still rely on manually designed action parameterizations, limiting their ability to produce the highly coordinated motions required in complex tasks. Motion planning can generate feasible trajectories, but the dynamics gap-stemming from control inaccuracies, contact uncertainties, and aerodynamic effects-often causes large deviations between planned and executed trajectories. In this work, we propose Dynamics-Aware Motion Manifold Primitives (DA-MMP), a motion generation framework for goal-conditioned dynamic manipulation, and instantiate it on a challenging real-world ring-tossing task. Our approach extends motion manifold primitives to variable-length trajectories through a compact parameterization and learns a high-quality manifold from a large-scale dataset of planned motions. Building on this manifold, a conditional flow matching model is trained in the latent space with a small set of real-world trials, enabling the generation of throwing trajectories that account for execution dynamics. Experiments show that our method can generate coordinated and smooth motion trajectories for the ring-tossing task. In real-world evaluations, it achieves high success rates and even surpasses the performance of trained human experts. Moreover, it generalizes to novel targets beyond the training range, indicating that it successfully learns the underlying trajectory-dynamics mapping.

Figures (7)

• Figure 1: Real-world ring tossing with trajectories synthesized by DA-MMP. The first line shows the overall sequence, where superimposed snapshots (light to dark) indicate temporal order of the coordinated throw. The second line illustrates three representative frames of the hitting process.
• Figure 2: Overview of DA-MMP. Stage I (blue): data collection from goal-manifold sampling, motion planning, and parameterization, yielding $90$k planned trajectories. Stage II (red/green): policy learning with an autoencoder to learn motion manifolds and a conditional flow-matching model for trajectory-dynamics mapping.
• Figure 3: Coordinate frames used for goal-manifold sampling. World $W$ is fixed to the ground; $B$ attaches to the robot base; the end-effector $E$ rigidly grasps the ring frame $R$ via ${}^E T_R$; the target frame $T$ sits at the cylinder top center. Inset: enlarged view of $E$ and $R$ for clarity.
• Figure 4: Illustration of basis functions used for trajectory parameterization. Left: normalized Gaussian bases over the phase. Right: gated bases obtained by multiplying the normalized bases with the polynomial gate $(s(1-s))^2$. For illustration, we show $K=6$.
• Figure 5: Experimental setup of real-world ring tossing.