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Model Predictive Parkour Control of a Monoped Hopper in Dynamically Changing Environments

Maximilian Albracht, Shivesh Kumar, Shubham Vyas, Frank Kirchner

TL;DR

The paper tackles the challenge of enabling a monoped hopper to traverse dynamically changing obstacle courses using Model Predictive Parkour Control (MPPC). It fuses mixed-integer impulse planning with a receding-horizon MPC framework and executes plans via a PD-controlled state machine with feedforward torques, yielding online re-planning and strong disturbance rejection. Key contributions include a complete MIP formulation for obstacle and restricted-area handling, a ballistic point-mass modeling approach, and experimental validation in static and dynamic parkour scenarios with real-time replanning. The results demonstrate robust, adaptive traversal in changing environments, pointing to potential 3D extensions and onboard perception integration for more autonomous legged locomotion.

Abstract

A great advantage of legged robots is their ability to operate on particularly difficult and obstructed terrain, which demands dynamic, robust, and precise movements. The study of obstacle courses provides invaluable insights into the challenges legged robots face, offering a controlled environment to assess and enhance their capabilities. Traversing it with a one-legged hopper introduces intricate challenges, such as planning over contacts and dealing with flight phases, which necessitates a sophisticated controller. A novel model predictive parkour controller is introduced, that finds an optimal path through a real-time changing obstacle course with mixed integer motion planning. The execution of this optimized path is then achieved through a state machine employing a PD control scheme with feedforward torques, ensuring robust and accurate performance.

Model Predictive Parkour Control of a Monoped Hopper in Dynamically Changing Environments

TL;DR

The paper tackles the challenge of enabling a monoped hopper to traverse dynamically changing obstacle courses using Model Predictive Parkour Control (MPPC). It fuses mixed-integer impulse planning with a receding-horizon MPC framework and executes plans via a PD-controlled state machine with feedforward torques, yielding online re-planning and strong disturbance rejection. Key contributions include a complete MIP formulation for obstacle and restricted-area handling, a ballistic point-mass modeling approach, and experimental validation in static and dynamic parkour scenarios with real-time replanning. The results demonstrate robust, adaptive traversal in changing environments, pointing to potential 3D extensions and onboard perception integration for more autonomous legged locomotion.

Abstract

A great advantage of legged robots is their ability to operate on particularly difficult and obstructed terrain, which demands dynamic, robust, and precise movements. The study of obstacle courses provides invaluable insights into the challenges legged robots face, offering a controlled environment to assess and enhance their capabilities. Traversing it with a one-legged hopper introduces intricate challenges, such as planning over contacts and dealing with flight phases, which necessitates a sophisticated controller. A novel model predictive parkour controller is introduced, that finds an optimal path through a real-time changing obstacle course with mixed integer motion planning. The execution of this optimized path is then achieved through a state machine employing a PD control scheme with feedforward torques, ensuring robust and accurate performance.
Paper Structure (20 sections, 15 equations, 9 figures, 3 tables, 1 algorithm)

This paper contains 20 sections, 15 equations, 9 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Sytem Setup
  3. Assumptions
  4. Parkour Environment
  5. Impulse Planning with Mixed Integer Optimization
  6. System Modeling
  7. Optimization Problem Formulation
  8. Dynamics
  9. Obstacles
  10. Collision Avoidance
  11. Restricted Areas
  12. Initial Guess
  13. Model Predictive Parkour Control Adaptation
  14. Behavior State Machine for Parkour
  15. Experimental Results
  16. ...and 5 more sections

Figures (9)

  • Figure 1: Combined snapshots of a parkour traversal.
  • Figure 2: Workspace idealization towards a cylindrical surface.
  • Figure 3: Exemplary parkour environment model
  • Figure 4: Leg orientation shift after take-off.
  • Figure 5: State machine to stabilize the behavior
  • ...and 4 more figures