Spectral Decomposition of Inverse Dynamics for Fast Exploration in Model-Based Manipulation

Solvin Sigurdson; Benjamin Riviere; Joel Burdick

cs.ROMar 29, 2026

Spectral Decomposition of Inverse Dynamics for Fast Exploration in Model-Based Manipulation

Authors: Solvin Sigurdson, Benjamin Riviere, Joel Burdick

Organizations: Department of Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125, USA · Department of Mechanical and Aerospace Engineering and the Department of Computer Science, New York University, New York City, NY 10012, USA

Abstract

Planning long duration robotic manipulation sequences is challenging because of the complexity of exploring feasible trajectories through nonlinear contact dynamics and many contact modes. Moreover, this complexity grows with the problem's horizon length. We propose a search tree method that generates trajectories using the spectral decomposition of the inverse dynamics equation. This equation maps actuator displacement to object displacement, and its spectrum is efficient for exploration because its components are orthogonal and they approximate the reachable set of the object while remaining dynamically feasible. These trajectories can be combined with any search based method, such as Rapidly-Exploring Random Trees (RRT), for long-horizon planning. Our method performs similarly to recent work in model-based planning for short-horizon tasks, and differentiates itself with its ability to solve long-horizon tasks: whereas existing methods fail, ours can generate 45 second duration, 10+ contact mode plans using 15 seconds of computation, demonstrating real-time capability in highly complex domains.

Figures & tables

Fig. 1 : Our method efficiently plans manipulation trajectories through several contact modes, discovering behavior like pushing, sliding, rolling, tumbling, and pivoting. In the physics-based simulator, an object (green prism) is moved with non-prehensile manipulation (red dot) through a contact-rich environment to a goal configuration.

Fig. 2 : Top left: Variables for the problem setup. Bottom right: Simple example of the fingertip exhibiting extrinsic dexterity in order to move an object through a maze.

Fig. 3 : An illustration of the fingertip controller. The dark green arrows are the linearized motion $\mathbf{v}_{i}$ projected forward $T_{\text{proj}}$ seconds, the gray arrows are the nonlinear motion, and the end of the red line is the fingertip reference point.

Fig. 4 : Left: For a single configuration where the object is pinned between the fingertip and the environment, proposed motion directions $\mathbf{v}_{i}$ are shows with red arrows, while the true reachable set for the center of the box is shown in pink. Right: Same as the left image except for a set of 5 different initial configurations to capture sampling different contacts between the object and manipulator. The approximate reachable set for the object’s COM is shown in gray, and efficiently captures a distinct subset of all possible motions in pink.

Fig. 5 : Pictoral representation of the MDP tree for a simple maze problem. In grey are the possible motion paths for the center of mass, while in dark green is a possible path chosen by the RRT algorithm.

Panel of Figure 6 — Fig. 6 : Short-Horizon Extrinsic Dexterity Tasks

Method	Metric	PP	CF	BR	BF	HP	PS
Ours	Success	1.0	1.0	1.0	1.0	1.0	1.0
	Time [s]	6.04	2.06	0.75	3.02	3.28	2.56
	Modes	2.6	4.7	2.5	6.1	6.7	6.0
	Branches	73.5	60.1	11.7	82.4	90.5	54.7
Bsl. 1 [ 17 ]	Success	0.9	0.05	0.0	0.25	$-$	$-$
Bsl. 1 [ 17 ]	Time [s]	3.1	17.9	$>$ 30.3	10.3	$-$	$-$

TABLE I : Performance on Short-Horizon Tasks

Panel of Figure 8 — Fig. 7 : Plots of tree expansion using Baseline 1 [ 17 ] for 2D and 3D pusher tasks. Tree branches shown in blue. 3D tasks collapse to breadth first search.

Panel of Figure 9 — Fig. 8 : Plots of tree expansion after 60s of computation in the 3D maze environment

Method	Success	Time [s]	Modes	Branches	Length [m]
Ours	1.0	15.0	9.34	436	3.90
Abl. 1	1.0	35.1	13.8	389	4.46
Abl. 2	0.96	20.55	10.8	492	3.32
Abl. 3	0.74	20.0	11.9	591	3.04
Abl. 4	0.88	13.3	31.1	634	3.15
Bsl. 2 ∗	0.0	$>$ 32.5	$\sim$	$\sim$	$\sim$

TABLE II : Ablation (Abl.) and Baseline (Bsl.) Performance. ∗ Ablations 1–4 have 50 trials and Baseline 2 has 10 trials.

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LAMP: Long-Horizon Adaptive Manipulation Planning for Multi-Robot Collaboration in Cluttered Space

Shuai Zhou, Yorai Shaoul, Jiaoyang Li

Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213, USA.

Long-Horizon Robotic Manipulation Robotic Manipulation Model-Based Planning Robot Motion Planning

Open paper AskPDF arXiv

Multi-robot manipulation requires jointly reasoning about contact formations, robot motions under coupled dynamics, and collision avoidance. Systematically searching over this large space is difficult and becomes increasingly intractable as the number of robots grows, the task horizon lengthens, or the scene becomes more densely cluttered. Existing approaches therefore either learn to solve the problem end-to-end via reinforcement learning or restrict planning to a simpler surrogate problem, such as planning object motions while learning short-horizon contact primitives. However, neither paradigm scales to the problem instances we target: long-horizon multi-robot manipulation in extremely dense environments. In this paper, we propose Long-horizon Adaptive Manipulation Planning (LAMP), a framework combining a generative model for manipulation with classical planning for long-horizon reasoning. We instantiate our framework with two algorithms leveraging insights from established planning techniques, A* and lazy search: LAMP-A*, which systematically searches over the coupled object-robot space, and LAMP-Lazy, a lazy planner that enables real-time replanning through deferred evaluation. Experiments in challenging simulated environments demonstrate that our approach solves complex long-horizon tasks in highly cluttered environments that prior methods cannot handle.

Abstract

Explore similar work

LAMP: Long-Horizon Adaptive Manipulation Planning for Multi-Robot Collaboration in Cluttered Space

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