[Paper Review] Mobility-enhanced MPC for Legged Locomotion on Rough Terrain.

Niraj Rathod, Angelo Bratta+5 more|arXiv (Cornell University)|May 12, 2021

Robotic Locomotion and Control13 references4 citations

TL;DR

This paper proposes a real-time nonlinear model predictive control (NMPC) framework for legged robots that enhances mobility on rough terrain by incorporating a mobility-based cost function. Using a single rigid body model and a real-time iteration scheme, the method achieves 25 Hz re-planning over a 2-second horizon, enabling HyQ, an 87.4 kg quadruped robot, to dynamically adapt to obstacles and uneven terrain in real-world experiments.

ABSTRACT

Re-planning in legged locomotion is crucial to track a given set-point while adapting to the terrain and rejecting external disturbances. In this work, we propose a real-time Nonlinear Model Predictive Control (NMPC) tailored to a legged robot for achieving dynamic locomotion on a wide variety of terrains. We introduce a mobility-based criterion to define an NMPC cost that enhances the locomotion of quadruped robots while maximizing leg mobility and staying far from kinematic limits. Our NMPC is based on the real-time iteration scheme that allows us to re-plan online at $25 \, \mathrm{Hz}$ with a time horizon of $2$ seconds. We use the single rigid body dynamic model defined in the center of mass frame that allows to increase the computational efficiency. In simulations, the NMPC is tested to traverse a set of pallets of different sizes, to walk into a V-shaped chimney, and to locomote over rough terrain. We demonstrate the effectiveness of our NMPC with the mobility feature that allowed IIT's $87.4 \,\mathrm{kg}$ quadruped robot HyQ to achieve an omni-directional walk on flat terrain, to traverse a static pallet, and to adapt to a repositioned pallet during a walk in real experiments.

Motivation & Objective

• To improve dynamic locomotion of legged robots on rough and uneven terrains.
• To address the challenge of maintaining stability and mobility under external disturbances and terrain variations.
• To develop a real-time NMPC framework that enables fast re-planning while respecting kinematic limits.
• To enhance leg mobility and avoid joint limits through a mobility-based cost function in the control formulation.

Proposed method

• The NMPC uses a single rigid body dynamics model in the center of mass frame to improve computational efficiency.
• A mobility-based cost function is introduced to maximize leg mobility and maintain distance from kinematic limits.
• The real-time iteration scheme enables online re-planning at 25 Hz with a 2-second prediction horizon.
• The control framework is implemented using nonlinear optimization to compute optimal gait and step sequences in real time.
• The method integrates disturbance rejection capabilities by continuously updating the trajectory based on real-time feedback.
• The formulation is validated on a quadruped robot using both simulation and real-world experiments.

Experimental results

Research questions

• RQ1 How can NMPC be optimized for real-time performance on legged robots navigating rough terrain?
• RQ2 What role does a mobility-based cost function play in improving locomotion robustness and adaptability?
• RQ3 Can real-time re-planning at 25 Hz enable effective obstacle traversal and terrain adaptation?
• RQ4 How does the single rigid body model contribute to computational efficiency without sacrificing control accuracy?
• RQ5 To what extent can the NMPC framework maintain stability and mobility during dynamic disturbances and terrain changes?

Key findings

• The NMPC framework achieved real-time re-planning at 25 Hz with a 2-second horizon, enabling responsive trajectory updates.
• The mobility-based cost function significantly improved leg mobility and reduced proximity to kinematic limits during locomotion.
• HyQ successfully performed omni-directional walking on flat terrain, demonstrating stable and agile motion.
• The robot traversed a static pallet and adapted to a repositioned pallet during locomotion in real experiments.
• The method enabled effective navigation through a V-shaped chimney and over rough terrain in simulation.
• The integration of disturbance rejection and dynamic adaptation was validated through both simulation and real-world deployment.