mlsanityData to 14 Oct 2026

Imitation Learning from MPC for Quadrupedal Multi-Gait Control

arXiv 2103.14331 ↗First posted 26 Mar 2021cs.RO cs.AI cs.SYcited by 18

On the map: Offline RL and imitation learning from data → Imitation learning methods

Abstract (arXiv)

We present a learning algorithm for training a single policy that imitates multiple gaits of a walking robot. To achieve this, we use and extend MPC-Net, which is an Imitation Learning approach guided by Model Predictive Control (MPC). The strategy of MPC-Net differs from many other approaches since its objective is to minimize the control Hamiltonian, which derives from the principle of optimality. To represent the policies, we employ a mixture-of-experts network (MEN) and observe that the performance of a policy improves if each expert of a MEN specializes in controlling exactly one mode of a hybrid system, such as a walking robot. We introduce new loss functions for single- and multi-gait policies to achieve this kind of expert selection behavior. Moreover, we benchmark our algorithm against Behavioral Cloning and the original MPC implementation on various rough terrain scenarios. We validate our approach on hardware and show that a single learned policy can replace its teacher to control multiple gaits.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data. Builds on 12 of its 37 references that are in the map. First posted on arXiv 26 Mar 2021.

Builds on

12 of 37 references.

Closest ancestors · 2

Same direction, newest first

  1. 2019MPC-Net: A First Principles Guided Policy Search11 Sep
  2. 2018An Algorithmic Perspective on Imitation Learning16 Nov

Other references · 10

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019Learning agile and dynamic motor skills for legged robotscited by 504
  3. 2019Learning by Cheatingcited by 383
  4. 2018Sim-to-Real: Learning Agile Locomotion For Quadruped Robotscited by 319
  5. 2020Learning Agile Robotic Locomotion Skills by Imitating Animalscited by 251
  6. 2018Learning to Walk via Deep Reinforcement Learningcited by 158
  7. 2019Policies Modulating Trajectory Generatorscited by 49
  8. 2016PLATO: Policy Learning using Adaptive Trajectory Optimizationcited by 24
  9. 2019Feedback MPC for Torque-Controlled Legged Robotscited by 21
  10. 2016An Efficient Optimal Planning and Control Framework For Quadrupedal Locomotioncited by 12

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 5; 2024: 2; 2025: 6; 2026: 1.

18 papers.

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  1. 2022Advanced Skills by Learning Locomotion and Local Navigation End-to-Endcited by 52
  2. 2024DiffuseLoco: Real-Time Legged Locomotion Control with Diffusion from Offline Datasetscited by 49
  3. 2022Learning Free Gait Transition for Quadruped Robots via Phase-Guided Controllercited by 29
  4. 2025Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classificationcited by 26
  5. 2021Demonstration-Efficient Guided Policy Search via Imitation of Robust Tube MPCcited by 11
  6. 2023Adversarial Imitation Learning from Visual Observations using Latent Informationcited by 11
  7. 2023Approximate non-linear model predictive control with safety-augmented neural networkscited by 9
  8. 2024Video2Reward: Generating Reward Function from Videos for Legged Robot Behavior Learningcited by 9
  9. 2021Learning Perceptual Locomotion on Uneven Terrains using Sparse Visual Observationscited by 5
  10. 2023Imitation Learning from Nonlinear MPC via the Exact Q-Loss and its Gauss-Newton Approximationcited by 5
  11. 2023DeepCPG Policies for Robot Locomotioncited by 4
  12. 2025ES-Parkour: Advanced Robot Parkour with Bio-inspired Event Camera and Spiking Neural Networkcited by 1
6 more
  1. 2025GRoQ-LoCO: Generalist and Robot-agnostic Quadruped Locomotion Control using Offline Datasetscited by 1
  2. 2023Efficient Deep Learning of Robust, Adaptive Policies using Tube MPC-Guided Data Augmentationcited by 0
  3. 2025Bridging the Sim-to-real Gap: A Control Framework for Imitation Learning of Model Predictive Controlcited by 0
  4. 2025Adaptive MPC-based quadrupedal robot control under periodic disturbancescited by 0
  5. 2025Unlocking the Potential of Soft Actor-Critic for Imitation Learningcited by 0
  6. 2026Bridging RL and MPC for mixed-integer optimal control with application to Formula 1 race strategiescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Imitating and Finetuning Model Predictive Control for Robust and Symmetric Quadrupedal Locomotion
  2. 2025Real-Time Gait Adaptation for Quadrupeds using Model Predictive Control and Reinforcement Learning
  3. 2026Learning Quadruped Walking from Seconds of Demonstration
  4. 2026MPC-Injection: Biasing Off-Policy Locomotion RL Toward Controller-Induced Behavior Basins
  5. 2023GAN-MPC: Training Model Predictive Controllers with Parameterized Cost Functions using Demonstrations from Non-identical Experts
  6. 2025Bootstrapped Model Predictive Control
  7. 2024RL-augmented MPC Framework for Agile and Robust Bipedal Footstep Locomotion Planning and Control
  8. 2025Residual MPC: Blending Reinforcement Learning with GPU-Parallelized Model Predictive Control