# Differentiable Constrained Imitation Learning for Robot Motion Planning and Control

arXiv: https://arxiv.org/abs/2210.11796 · HTML: https://mlsanity.com/paper/2210.11796/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Imitation and offline RL for driving, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Placed in

- Offline RL and imitation learning from data / [Imitation and offline RL for driving](https://mlsanity.com/offlinerl/imitation-and-offline-rl-for-driving/)

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [ChauffeurNet: Learning to Drive by Imitating the Best and Synthesizing the Worst](https://mlsanity.com/paper/1812.03079/) (2018)
- [Exploring the Limitations of Behavior Cloning for Autonomous Driving](https://mlsanity.com/paper/1904.08980/) (2019)
- [End-to-end Interpretable Neural Motion Planner](https://mlsanity.com/paper/2101.06679/) (2021)
- [End-to-End Urban Driving by Imitating a Reinforcement Learning Coach](https://mlsanity.com/paper/2108.08265/) (2021)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Learning from All Vehicles](https://mlsanity.com/paper/2203.11934/) (2022)
- [Reward (Mis)design for Autonomous Driving](https://mlsanity.com/paper/2104.13906/) (2021)
- [SafetyNet: Safe planning for real-world self-driving vehicles using machine-learned policies](https://mlsanity.com/paper/2109.13602/) (2021)
- [Jointly Learnable Behavior and Trajectory Planning for Self-Driving Vehicles](https://mlsanity.com/paper/1910.04586/) (2019)
- [UMBRELLA: Uncertainty-Aware Model-Based Offline Reinforcement Learning Leveraging Planning](https://mlsanity.com/paper/2111.11097/) (2021)
- [Exploring Imitation Learning for Autonomous Driving with Feedback Synthesizer and Differentiable Rasterization](https://mlsanity.com/paper/2103.01882/) (2021)
- [Driving in Real Life with Inverse Reinforcement Learning](https://mlsanity.com/paper/2206.03004/) (2022)
- [Semi-Supervised Trajectory-Feedback Controller Synthesis for Signal Temporal Logic Specifications](https://mlsanity.com/paper/2202.01997/) (2022)
- [Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Driving](https://mlsanity.com/paper/2203.02401/) (2022)
- [Self-Supervised Action-Space Prediction for Automated Driving](https://mlsanity.com/paper/2109.10024/) (2021)
- [Sample-Specific Output Constraints for Neural Networks](https://mlsanity.com/paper/2003.10258/) (2020)
- [Online Motion Planning based on Nonlinear Model Predictive Control with Non-Euclidean Rotation Groups](https://mlsanity.com/paper/2006.03534/) (2020)

## Built on by (most cited first, 7 of 7)

- [Energy-based Potential Games for Joint Motion Forecasting and Control](https://mlsanity.com/paper/2312.01811/) (2023)
- [On a Connection between Differential Games, Optimal Control, and Energy-based Models for Multi-Agent Interactions](https://mlsanity.com/paper/2308.16539/) (2023)
- [LoRD: Adapting Differentiable Driving Policies to Distribution Shifts](https://mlsanity.com/paper/2410.09681/) (2024)
- [Non-differentiable Reward Optimization for Diffusion-based Autonomous Motion Planning](https://mlsanity.com/paper/2507.12977/) (2025)
- [Integrating Decision-Making Into Differentiable Optimization Guided Learning for End-to-End Planning of Autonomous Vehicles](https://mlsanity.com/paper/2412.01234/) (2024)
- [Zero-shot adaptable task planning for autonomous construction robots: a comparative study of lightweight single and multi-AI agent systems](https://mlsanity.com/paper/2601.14091/) (2026)
- [Infeasible optimization problems and the hierarchical augmented Lagrangian method in imitation learning](https://mlsanity.com/paper/2606.00730/) (2026)

## Abstract (arXiv)

Motion planning and control are crucial components of robotics applications like automated driving. Here, spatio-temporal hard constraints like system dynamics and safety boundaries (e.g., obstacles) restrict the robot's motions. Direct methods from optimal control solve a constrained optimization problem. However, in many applications finding a proper cost function is inherently difficult because of the weighting of partially conflicting objectives. On the other hand, Imitation Learning (IL) methods such as Behavior Cloning (BC) provide an intuitive framework for learning decision-making from offline demonstrations and constitute a promising avenue for planning and control in complex robot applications. Prior work primarily relied on soft constraint approaches, which use additional auxiliary loss terms describing the constraints. However, catastrophic safety-critical failures might occur in out-of-distribution (OOD) scenarios. This work integrates the flexibility of IL with hard constraint handling in optimal control. Our approach constitutes a general framework for constraint robotic motion planning and control, as well as traffic agent simulation, whereas we focus on mobile robot and automated driving applications. Hard constraints are integrated into the learning problem in a differentiable manner, via explicit completion and gradient-based correction. Simulated experiments of mobile robot navigation and automated driving provide evidence for the performance of the proposed method.