STAMP: Differentiable Task and Motion Planning via Stein Variational Gradient Descent

STAMP: Differentiable Task and Motion Planning via Stein Variational Gradient Descent
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Original Paper
Planning for many manipulation tasks, such as using tools or assembling parts, often requires both symbolic and geometric reasoning. Task and Motion Planning (TAMP) algorithms typically solve these problems by conducting a tree search over high-level task sequences while checking for kinematic and dynamic feasibility. This can be inefficient as the width of the tree can grow exponentially with the number of possible actions and objects. In this paper, we propose a novel approach to TAMP that relaxes discrete-and-continuous TAMP problems into inference problems on a continuous domain. Our method, Stein Task and Motion Planning (STAMP) subsequently solves this new problem using a gradient-based variational inference algorithm called Stein Variational Gradient Descent, by obtaining gradients from a parallelized differentiable physics simulator. By introducing relaxations to the discrete variables, leveraging parallelization, and approaching TAMP as an Bayesian inference problem, our method is able to efficiently find multiple diverse plans in a single optimization run. We demonstrate our method on two TAMP problems and benchmark them against existing TAMP baselines.

Summary Notes

Introducing STAMP: A New Era in Task and Motion Planning

In the evolving landscape of artificial intelligence and robotics, Task and Motion Planning (TAMP) is a vital area, blending logical problem-solving with physical constraints to create executable plans for robots.
Traditional strategies, often based on tree search methods, face challenges in efficiency and in producing a variety of solutions.
This blog post introduces a novel approach, Stein Task and Motion Planning (STAMP), which uses Stein Variational Gradient Descent (SVGD) and differentiable physics simulators to improve TAMP, making it more efficient and varied in its solutions.

Exploring the TAMP Challenge

TAMP combines discrete, symbolic actions with continuous motion plans, requiring both logic and geometric reasoning.
Traditional methods are somewhat effective but often inefficient and limited to producing a single, fixed plan.
This becomes a problem in dynamic settings where flexibility and multiple plan options are essential.

How STAMP Offers a Solution

STAMP represents a significant shift in solving TAMP problems by treating them as Bayesian inference challenges over continuous variables. Below are the key elements and benefits of STAMP:

SVGD: The Heart of STAMP

  • Stein Variational Gradient Descent (SVGD) uses a group of particles to estimate target distributions for efficient inference.
  • SVGD benefits from gradient updates, made more effective with gradients from differentiable physics simulators.

Differentiable Physics Simulators: The Efficiency Boosters

  • These simulators calculate gradients relative to system parameters, aiding in optimizing physical simulations.
  • They're essential in STAMP for making real-time adjustments and improvements in motion plans.

STAMP's Innovative Approach

  • Bayesian Inference for TAMP: Transforms discrete actions into a continuous space suitable for SVGD.
  • Gradient-Based Optimization: Uses gradients from physics simulators to refine task and motion plans.
  • Parallelization: Enhances inference efficiency, enabling scalability and real-time applications.

Implementing STAMP: Insights and Results

Key Implementation Aspects

  • Dynamic Motion Primitives (DMPs) for motion planning and Warp, a parallelizable simulator, for efficient gradient calculations.

Experimental Success

  • STAMP was tested on complex problems like billiards and block-pushing, surpassing traditional methods in solution diversity and efficiency.

The Benefits and What's Next for STAMP

STAMP advances TAMP significantly by providing:
  • Efficiency and Diversity: It quickly generates multiple viable plans, addressing traditional TAMP methods' limitations.
  • Scalability: Its ability to handle more complex and larger-scale TAMP challenges presents new research and application possibilities.
The future of TAMP is promising with STAMP, indicating potential for more sophisticated applications and further technological advancements.


Stein Task and Motion Planning (STAMP) marks a breakthrough in robotics and AI, offering an efficient and diverse approach to task and motion planning.
By incorporating advanced inference techniques and differentiable simulation capabilities, STAMP surpasses traditional TAMP methods and paves the way for more complex planning tasks.
With continuing developments in SVGD and differentiable physics simulators, the future of robotic planning is set to become even more efficient and adaptable.

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