# Multimodal Trajectory Optimization for Motion Planning

arXiv: https://arxiv.org/abs/2003.07054 · HTML: https://mlsanity.com/paper/2003.07054/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2020.

## Built on by (most cited first, 12 of 12)

- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [Learning Implicit Priors for Motion Optimization](https://mlsanity.com/paper/2204.05369/) (2022)
- [Discovering Diverse Solutions in Deep Reinforcement Learning by Maximizing State-Action-Based Mutual Information](https://mlsanity.com/paper/2103.07084/) (2021)
- [Motion Planning by Learning the Solution Manifold in Trajectory Optimization](https://mlsanity.com/paper/2107.05842/) (2021)
- [Constrained Stein Variational Trajectory Optimization](https://mlsanity.com/paper/2308.12110/) (2023)
- [How to Fill the Optimum Set? Population Gradient Descent with Harmless Diversity](https://mlsanity.com/paper/2202.08376/) (2022)
- [Tensor Train for Global Optimization Problems in Robotics](https://mlsanity.com/paper/2206.05077/) (2022)
- [Global Tensor Motion Planning](https://mlsanity.com/paper/2411.19393/) (2024)
- [Shadow Program Inversion with Differentiable Planning: A Framework for Unified Robot Program Parameter and Trajectory Optimization](https://mlsanity.com/paper/2409.08678/) (2024)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Optimal Motion Planning using Finite Fourier Series in a Learning-based Collision Field](https://mlsanity.com/paper/2312.09073/) (2023)
- [GRACE: Gradient-Free Robot Action Generation via Combined Diffusion-MPPI Posterior Mean Estimation](https://mlsanity.com/paper/2607.21661/) (2026)

## Abstract (arXiv)

Existing motion planning methods often have two drawbacks: 1) goal configurations need to be specified by a user, and 2) only a single solution is generated under a given condition. In practice, multiple possible goal configurations exist to achieve a task. Although the choice of the goal configuration significantly affects the quality of the resulting trajectory, it is not trivial for a user to specify the optimal goal configuration. In addition, the objective function used in the trajectory optimization is often non-convex, and it can have multiple solutions that achieve comparable costs. In this study, we propose a framework that determines multiple trajectories that correspond to the different modes of the cost function. We reduce the problem of identifying the modes of the cost function to that of estimating the density induced by a distribution based on the cost function. The proposed framework enables users to select a preferable solution from multiple candidate trajectories, thereby making it easier to tune the cost function and obtain a satisfactory solution. We evaluated our proposed method with motion planning tasks in 2D and 3D space. Our experiments show that the proposed algorithm is capable of determining multiple solutions for those tasks.