[Paper Review] Computed-torque method for the control of a 2 DOF orthosis actuated through pneumatic artificial muscles: a specific case for the rehabilitation of the lower limb

Flavio Prattico, Mohd Azuwan Mat Dzahir+1 more|arXiv (Cornell University)|Apr 24, 2014

Prosthetics and Rehabilitation Robotics17 references4 citations

TL;DR

This paper proposes a computed-torque control method for a 2-DOF lower limb orthosis (AIRGAIT) actuated by custom-made pneumatic artificial muscles (PAMs). By modeling PAM nonlinearity via polynomial fits and using Newton-Euler dynamics to compute joint torques, the system achieves accurate trajectory tracking across sinusoidal, square, and random walking inputs, with minimal delay even at 1 Hz (equivalent to 1.4 m/s gait speed), demonstrating high-accuracy, real-time control without feedback-based tuning.

ABSTRACT

In this paper we give a new control model based on the so called computed-torque method for the control of a 2 degrees of freedom orthosis for the rehabilitation of the lower limb, the AIRGAIT exoskeleton's leg orthosis. The actuation of the AIRGAIT is made through self-made pneumatic muscles. For this reason this work starts with the static and dynamic characterization of our pneumatic muscles. The followed approach is based on the analytical description of the system. For this, we describe the pneumatic muscles behaviour with an easy-invertible polynomial fit function in order to model its non-linear trend. We give a geometrical model of the mechanical system to compute the length between the attachments of the pneumatic muscles to the structure for every angles assumed by the two joints. We evaluate through Newton-Euler equation the couples at the joints for each values of the angles. At last we show some validation tests in order to characterize the functioning of the proposed control model on the actuation of the orthosis.

Motivation & Objective

• To develop a precise, feedforward control strategy for a 2-DOF lower limb exoskeleton (AIRGAIT) actuated by self-made pneumatic artificial muscles (PAMs).
• To address the challenge of controlling highly nonlinear PAMs in a rehabilitation context without relying on feedback-based control methods.
• To validate the control model across diverse dynamic trajectories, including sinusoidal, square, and random walking patterns, to assess real-time performance and tracking accuracy.
• To demonstrate the feasibility of applying the computed-torque method to a multi-degree-of-freedom PAM-driven orthosis, a novel application in the field.

Proposed method

• Model the nonlinear force-contraction behavior of self-fabricated PAMs using a polynomial fit function derived from static characterization data.
• Develop a geometric model to compute the effective muscle length based on joint angles, enabling accurate torque estimation.
• Apply Newton-Euler dynamics to analytically compute the required joint torques for desired trajectories, forming the core of the computed-torque control framework.
• Implement a feedforward control architecture that uses the computed torque values to drive the PAMs via pressure regulation, without relying on feedback correction.
• Use LabVIEW and RIO modules to interface the control system, sending input signals and acquiring real-time joint angle measurements via potentiometers.
• Validate the model using multiple trajectory types: sinusoidal (0.05–1 Hz), square-wave, and random walk inputs, with path tracking evaluated at the ankle end-effector.

Experimental results

Research questions

• RQ1 Can the computed-torque method effectively control a 2-DOF lower limb orthosis actuated by nonlinear pneumatic artificial muscles?
• RQ2 How accurately can the system track dynamic trajectories such as sinusoidal, square, and random walking patterns without feedback-based tuning?
• RQ3 To what extent does the analytical modeling of PAM nonlinearity and joint dynamics improve control performance compared to simpler control schemes?
• RQ4 What is the maximum achievable gait frequency (in Hz) for which the system maintains acceptable tracking accuracy?
• RQ5 Can the system accurately reproduce complex, real-world walking-like trajectories in a clinical rehabilitation context?

Key findings

• The system achieved near-ideal tracking of sinusoidal trajectories up to 1 Hz, corresponding to a gait speed of 1.4 m/s, which matches the pace of a healthy individual.
• At 1 Hz, the system exhibited only a minor delay, demonstrating robustness and real-time capability under high-frequency demand.
• For a 0.5 Hz square wave input, the system reached the target angle in an average of 0.1 seconds per transition, indicating fast response and minimal lag.
• The system accurately followed a random walk trajectory with a 2-second period, confirming its ability to handle complex, non-repeating motion patterns.
• Ankle path tracking in 2D space confirmed that the end-effector followed the desired trajectory with high fidelity, validating the overall kinematic and dynamic model accuracy.
• The computed-torque method enabled high-accuracy, feedforward control of the PAM-driven orthosis without feedback correction, marking a novel application in lower limb rehabilitation robotics.