Task-Space Motion-Force Nonlinear Model Predictive Control for Precise and Compliant Control under Uncertainties

Quang-Nam Nguyen; Ludovic Righetti

cs.ROOct 12, 2026

Task-Space Motion-Force Nonlinear Model Predictive Control for Precise and Compliant Control under Uncertainties

Authors: Quang-Nam Nguyen, Ludovic Righetti

Organizations: Machines in Motion Laboratory, Center for Robotics and Embodied Intelligence, New York University (NYU), USA. · Artificial and Natural Intelligence Toulouse Institute (ANITI), France.

Abstract

In Nonlinear Model Predictive Control (NMPC), the control law is implicitly determined by the solution of an Optimal Control Problem (OCP). Consequently, OCP design is often tailored to specific platforms and tasks, demanding extensive expert knowledge and tuning effort. To address this, we propose a unified NMPC framework that directly plans and controls the robot joints subject to task-space motion and force requirements and is capable of seamlessly generalizing across multiple robotic platforms and diverse tasks. Furthermore, optimization-based methods often treat interactions as rigid contacts, making the torque solution sensitive to the modeling errors of the robot dynamics and the environment. We study the intrinsic task-space impedance of our proposed controller, its partial contraction for differential stability and differential passivity under unmodeled interactions. As a result, our framework enables closing the force-feedback loop in the high-level planning layer to achieve precise motion-force tracking performance, addressing the long-standing challenge of force-feedback NMPC. Finally, we validate our framework on physical hardware, demonstrating hybrid motion-force control on a redundant manipulator and compliant locomotion on a quadruped, while preserving core NMPC advantages such as hard constraint satisfaction, optimal redundancy exploitation, and real-time planning under unforeseen interactions.

Figures & tables

Fig. 1: Our force feedback IA-NMPC performs safe and precise motion-force control tasks: (a) drawing on a deformable surface, (b) massaging, and (c) $SE(3)$ manipulation of an unknown heavy object. Without force feedback, our I-NMPC creates robust, compliant behaviors on a quadruped: (d) walking through unknown terrains, and (e) pulling human on a chair.

Fig. 2: Task-space Impedance-Admittance NMPC Architecture

Fig. 3: Simplified diagram of Impedance-Admittance NMPC

Panel of Figure 4 — Fig. 4: Press test: contact forces when changing the relative goal pose $\Delta z$ , the $z$ component of weight matrix $Q$ , and the end-effector’s position.

Fig. 5: Comparison of force tracking precision between different methods.

Panel of Figure 6 — Fig. 6: Drawing under disturbances with real-time constraint addition.

Method	IA-NMPC (ours)	A-NMPC (ours)	Admittance IK	Admittance ID	Direct Force Control
(Mode)	(Pure Torque)	(Position)	(Position)	(Torque + PD)	(Torque + PD)
Board	$0.98\pm 0.23$ N (0.65mm)	$0.98\pm 0.27$ N (0.05mm)	$0.98\pm 0.15$ N (0.02mm)	$0.99\pm 0.25$ N (6.86mm)	$1.11\pm 0.29$ N (6.09mm)
Paper	$2.00\pm 0.12$ N (0.87mm)	$2.00\pm 0.12$ N (0.17mm)	$2.00\pm 0.12$ N (0.16mm)	$2.00\pm 0.16$ N (6.11mm)	$2.81\pm 0.87$ N (5.67mm)
Balloon	$0.50\pm 0.08$ N (1.48mm)	$0.50\pm 0.09$ N (0.37mm)	$0.50\pm 0.12$ N (0.11mm)	$0.49\pm 0.10$ N (6.42mm)	$2.06\pm 1.08$ N (8.80mm)
Massage	$10.0\pm 0.2$ N (0.87mm)	$10.0\pm 0.2$ N (0.43mm)	$10.0\pm 0.5$ N (0.24mm)	$10.0\pm 1.1$ N (11.9mm)	$10.1\pm 0.9$ N (7.16mm)

TABLE I: Contact force and position tracking precision on different surfaces and desired force:

\bigcirc

Board (1.0N) –

\heartsuit

Paper (2.0N) –

\heartsuit

Balloon (0.5N) –

\infty

Box massage (10.0N)

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