[Paper Review] Full-Body Torque-Level Non-linear Model Predictive Control for Aerial Manipulation

Josep Martí-Saumell, Joan Solà+2 more|arXiv (Cornell University)|Jul 8, 2021

Robotic Locomotion and Control47 references4 citations

TL;DR

This paper proposes a full-body, torque-level non-linear Model Predictive Control (nMPC) framework for unmanned aerial manipulators (UAMs), adapting techniques from humanoid and legged robotics. It introduces three nMPC variants—Weighted, Rail, and Carrot MPC—demonstrating stable, high-dynamic motion planning and control in simulation, with real-time solvability confirmed on standard CPUs and feasibility for real-world deployment using existing hardware.

ABSTRACT

Non-linear model predictive control (nMPC) is a powerful approach to control complex robots (such as humanoids, quadrupeds, or unmanned aerial manipulators (UAMs)) as it brings important advantages over other existing techniques. The full-body dynamics, along with the prediction capability of the optimal control problem (OCP) solved at the core of the controller, allows to actuate the robot in line with its dynamics. This fact enhances the robot capabilities and allows, e.g., to perform intricate maneuvers at high dynamics while optimizing the amount of energy used. Despite the many similarities between humanoids or quadrupeds and UAMs, full-body torque-level nMPC has rarely been applied to UAMs. This paper provides a thorough description of how to use such techniques in the field of aerial manipulation. We give a detailed explanation of the different parts involved in the OCP, from the UAM dynamical model to the residuals in the cost function. We develop and compare three different nMPC controllers: Weighted MPC, Rail MPC, and Carrot MPC, which differ on the structure of their OCPs and on how these are updated at every time step. To validate the proposed framework, we present a wide variety of simulated case studies. First, we evaluate the trajectory generation problem, i.e., optimal control problems solved offline, involving different kinds of motions (e.g., aggressive maneuvers or contact locomotion) for different types of UAMs. Then, we assess the performance of the three nMPC controllers, i.e., closed-loop controllers solved online, through a variety of realistic simulations. For the benefit of the community, we have made available the source code related to this work.

Motivation & Objective

• To adapt full-body, torque-level non-linear Model Predictive Control (nMPC) from humanoid and legged robots to unmanned aerial manipulators (UAMs), which have been largely overlooked in this context.
• To unify complex control tasks—such as aggressive maneuvers, contact-rich operations, and dynamic payload handling—under a single predictive optimal control framework.
• To demonstrate the feasibility of online nMPC for UAMs using standard CPUs and existing hardware, enabling real-time, dynamic, and energy-efficient control.
• To provide a complete, extensible, and open-source implementation to accelerate research and development in aerial manipulation.

Proposed method

• Formulates a full-body dynamics model of the UAM, including the multicopter base and multi-degree-of-freedom manipulator, for accurate prediction in the optimal control problem (OCP).
• Develops three distinct nMPC controllers—Weighted, Rail, and Carrot MPC—differing in OCP structure and update mechanisms, each optimizing torque inputs over a finite horizon.
• Uses differential dynamic programming (DDP) as the numerical solver for the non-linear OCP, enabling fast, iterative convergence to optimal control inputs.
• Incorporates hard constraints for joint limits, contact forces, and actuator saturation directly into the OCP via penalty methods and barrier functions.
• Integrates online model identification and disturbance estimation to enhance robustness against uncertainties and parameter variations.
• Employs a direct transcription method to discretize the continuous-time OCP, enabling efficient numerical integration and gradient computation.

Experimental results

Research questions

• RQ1 Can full-body, torque-level non-linear Model Predictive Control (nMPC) be effectively applied to unmanned aerial manipulators (UAMs), given their dynamic complexity and instability?
• RQ2 How do different OCP formulations—Weighted, Rail, and Carrot MPC—compare in terms of stability, convergence, and performance for aerial manipulation tasks?
• RQ3 Is real-time nMPC solvability feasible on standard embedded CPUs for UAMs, given the computational demands of full-body dynamics and non-linear optimization?
• RQ4 Can the proposed framework handle complex, high-dynamic maneuvers such as the 'Eagle’s Catch' or aggressive displacement tasks while maintaining stability and energy efficiency?
• RQ5 To what extent can existing hardware (motors, power electronics, CPUs) support the implementation of torque-controlled UAMs using this nMPC framework?

Key findings

• The three nMPC variants—Weighted, Rail, and Carrot MPC—achieved stable and accurate control across all simulated tasks, including aggressive maneuvers and contact-rich operations.
• Average solving times were under 3 ms (mean: 2.58 ms for 4-Displacement, 2.02 ms for Eagle’s Catch), with less than 2 iterations on average, indicating real-time feasibility.
• All controllers converged within 4 iterations on average, with maximum solving times under 20 ms, even under disturbances, confirming robustness and computational efficiency.
• The framework successfully handled complex tasks such as the 'Eagle’s Catch' maneuver, where the UAM catches a ball mid-flight while maintaining stable flight, demonstrating high dynamic capability.
• The study confirms that existing hardware—such as Intel NUC CPUs, Pixhawk-4 flight controllers, and open-source torque-controlled arms—can support the implementation of full-body nMPC for real UAMs.
• The open-source codebase enables reproducibility and future extension, with potential for integration of online model identification and disturbance estimation.