# Interactive multi-modal motion planning with Branch Model Predictive Control

arXiv: https://arxiv.org/abs/2109.05128 · HTML: https://mlsanity.com/paper/2109.05128/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2021.

## Built on by (most cited first, 21 of 21)

- [ScePT: Scene-consistent, Policy-based Trajectory Predictions for Planning](https://mlsanity.com/paper/2206.13387/) (2022)
- [DiffStack: A Differentiable and Modular Control Stack for Autonomous Vehicles](https://mlsanity.com/paper/2212.06437/) (2022)
- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Active Uncertainty Reduction for Safe and Efficient Interaction Planning: A Shielding-Aware Dual Control Approach](https://mlsanity.com/paper/2302.00171/) (2023)
- [Interactive Joint Planning for Autonomous Vehicles](https://mlsanity.com/paper/2310.18301/) (2023)
- [Active Uncertainty Reduction for Human-Robot Interaction: An Implicit Dual Control Approach](https://mlsanity.com/paper/2202.07720/) (2022)
- [Blending Data-Driven Priors in Dynamic Games](https://mlsanity.com/paper/2402.14174/) (2024)
- [Predictive Control for Autonomous Driving with Uncertain, Multi-modal Predictions](https://mlsanity.com/paper/2310.20561/) (2023)
- [Proactive Emergency Collision Avoidance for Automated Driving in Highway Scenarios](https://mlsanity.com/paper/2310.17381/) (2023)
- [A First Physical-World Trajectory Prediction Attack via LiDAR-induced Deceptions in Autonomous Driving](https://mlsanity.com/paper/2406.11707/) (2024)
- [Traffic-Rule-Compliant Trajectory Repair via Satisfiability Modulo Theories and Reachability Analysis](https://mlsanity.com/paper/2412.15837/) (2024)
- [Generative AI for Autonomous Driving: A Review](https://mlsanity.com/paper/2505.15863/) (2025)
- [IR-STP: Enhancing Autonomous Driving with Interaction Reasoning in Spatio-Temporal Planning](https://mlsanity.com/paper/2311.02850/) (2023)
- [EP-Diffuser: An Efficient Diffusion Model for Traffic Scene Generation and Prediction via Polynomial Representations](https://mlsanity.com/paper/2504.05422/) (2025)
- [Scalable Multi-modal Model Predictive Control via Duality-based Interaction Predictions](https://mlsanity.com/paper/2402.01116/) (2024)
- [Model Predictive Control for Crowd Navigation via Learning-Based Trajectory Prediction](https://mlsanity.com/paper/2508.07079/) (2025)
- [An Evolutionary Game-Theoretic Merging Decision-Making Considering Social Acceptance for Autonomous Driving](https://mlsanity.com/paper/2508.07080/) (2025)
- [Safe and Nonconservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barriers](https://mlsanity.com/paper/2509.07464/) (2025)
- [Interactive Trajectory Planning with Learning-based Distributionally Robust Model Predictive Control and Markov Systems](https://mlsanity.com/paper/2605.07768/) (2026)
- [Still Camouflage, Moving Illusion: View-Induced Trajectory Manipulation in Autonomous Driving](https://mlsanity.com/paper/2605.12743/) (2026)
- [Kernel-Based Metrics Learning for Uncertain Opponent Vehicle Trajectory Prediction in Autonomous Racing](https://mlsanity.com/paper/2609.17147/) (2026)

## Abstract (arXiv)

Motion planning for autonomous robots and vehicles in presence of uncontrolled agents remains a challenging problem as the reactive behaviors of the uncontrolled agents must be considered. Since the uncontrolled agents usually demonstrate multimodal reactive behavior, the motion planner needs to solve a continuous motion planning problem under these behaviors, which contains a discrete element. We propose a branch Model Predictive Control (MPC) framework that plans over feedback policies to leverage the reactive behavior of the uncontrolled agent. In particular, a scenario tree is constructed from a finite set of policies of the uncontrolled agent, and the branch MPC solves for a feedback policy in the form of a trajectory tree, which shares the same topology as the scenario tree. Moreover, coherent risk measures such as the Conditional Value at Risk (CVaR) are used as a tuning knob to adjust the tradeoff between performance and robustness. The proposed branch MPC framework is tested on an overtake and lane change task and a merging task for autonomous vehicles in simulation, and on the motion planning of an autonomous quadruped robot alongside an uncontrolled quadruped in experiments. The result demonstrates interesting human-like behaviors, achieving a balance between safety and performance.