Concurrent Adaptive Control for a Robotic Leg Prosthesis via a Neuromuscular-Force-Based Impedance Method and Human-in-the-Loop Optimization
This paper proposes an adaptive human–robot concurrent control scheme that achieves the appropriate gait trajectory for a robotic leg prosthesis to improve the wearer’s comfort in various tasks. To accommodate different wearers, a neuromuscular-force-based impedance method was developed using muscle...
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| description | This paper proposes an adaptive human–robot concurrent control scheme that achieves the appropriate gait trajectory for a robotic leg prosthesis to improve the wearer’s comfort in various tasks. To accommodate different wearers, a neuromuscular-force-based impedance method was developed using muscle activation to reshape gait trajectory. To eliminate the use of sensors for torque measurement, a disturbance observer was established to estimate the interaction force between the human residual limb and the prosthetic receptacle. The cost function was combined with the interaction force and tracking errors of the joints. We aim to reduce the cost function by minimally changing the control weight of the gait trajectory generated by the Central Pattern Generator (CPG). The control scheme was primarily based on human-in-the-loop optimization to search for a suitable control weight to regenerate the appropriate gait trajectory. To handle the uncertainties and unknown coupling of the motors, an adaptive law was designed to estimate the unknown parameters of the system. Through a stability analysis, the control framework was verified by semi-globally uniformly ultimately bounded stability. Experimental results are discussed, and the effectiveness of the adaptive control framework is demonstrated. In Case 1, the mean error (MEAN) of the tracking performance was <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.6</mn><mo>°</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.3</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively. And the minimized mean square errors (MSEs) of the tracking performance were <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.3</mn><mo>°</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.8</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively. In Case 2, the mean error (MEAN) of the tracking performance is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.7</mn><mo>°</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.1</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively. And the minimized mean square errors (MSEs) of the tracking performance are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.8</mn><mo>°</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.4</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively. In Case 3, the mean errors (MEANs) of the tracking performance for subject1 and 2 are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.4</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.9</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.4</mn><mo>°</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.2</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.8</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.1</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively. The minimized mean square errors (MSEs) of the tracking performance for subject1 and 2 were <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.6</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.3</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.6</mn><mo>°</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.3</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.7</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.2</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively. |
| format | Article |
| id | doaj-art-38b94c58eced4991a5c8fd6c9cf76610 |
| institution | DOAJ |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-38b94c58eced4991a5c8fd6c9cf766102025-08-20T03:04:40ZengMDPI AGApplied Sciences2076-34172025-07-011515812610.3390/app15158126Concurrent Adaptive Control for a Robotic Leg Prosthesis via a Neuromuscular-Force-Based Impedance Method and Human-in-the-Loop OptimizationMing Pi0School of Information and Control Engineering, Southwest University of Science and Technology, Mianyang 621010, ChinaThis paper proposes an adaptive human–robot concurrent control scheme that achieves the appropriate gait trajectory for a robotic leg prosthesis to improve the wearer’s comfort in various tasks. To accommodate different wearers, a neuromuscular-force-based impedance method was developed using muscle activation to reshape gait trajectory. To eliminate the use of sensors for torque measurement, a disturbance observer was established to estimate the interaction force between the human residual limb and the prosthetic receptacle. The cost function was combined with the interaction force and tracking errors of the joints. We aim to reduce the cost function by minimally changing the control weight of the gait trajectory generated by the Central Pattern Generator (CPG). The control scheme was primarily based on human-in-the-loop optimization to search for a suitable control weight to regenerate the appropriate gait trajectory. To handle the uncertainties and unknown coupling of the motors, an adaptive law was designed to estimate the unknown parameters of the system. Through a stability analysis, the control framework was verified by semi-globally uniformly ultimately bounded stability. Experimental results are discussed, and the effectiveness of the adaptive control framework is demonstrated. In Case 1, the mean error (MEAN) of the tracking performance was <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.6</mn><mo>°</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.3</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively. And the minimized mean square errors (MSEs) of the tracking performance were <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.3</mn><mo>°</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.8</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively. In Case 2, the mean error (MEAN) of the tracking performance is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.7</mn><mo>°</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.1</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively. And the minimized mean square errors (MSEs) of the tracking performance are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.8</mn><mo>°</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.4</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively. In Case 3, the mean errors (MEANs) of the tracking performance for subject1 and 2 are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.4</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.9</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.4</mn><mo>°</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.2</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.8</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.1</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively. The minimized mean square errors (MSEs) of the tracking performance for subject1 and 2 were <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.6</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.3</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.6</mn><mo>°</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.3</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.7</mn><mo>°</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.2</mn><mo>°</mo></mrow></semantics></math></inline-formula>, respectively.https://www.mdpi.com/2076-3417/15/15/8126robotic leg prosthesismulti-task walkingconcurrent adaptive controlhuman-in-the-loop optimization |
| spellingShingle | Ming Pi Concurrent Adaptive Control for a Robotic Leg Prosthesis via a Neuromuscular-Force-Based Impedance Method and Human-in-the-Loop Optimization Applied Sciences robotic leg prosthesis multi-task walking concurrent adaptive control human-in-the-loop optimization |
| title | Concurrent Adaptive Control for a Robotic Leg Prosthesis via a Neuromuscular-Force-Based Impedance Method and Human-in-the-Loop Optimization |
| title_full | Concurrent Adaptive Control for a Robotic Leg Prosthesis via a Neuromuscular-Force-Based Impedance Method and Human-in-the-Loop Optimization |
| title_fullStr | Concurrent Adaptive Control for a Robotic Leg Prosthesis via a Neuromuscular-Force-Based Impedance Method and Human-in-the-Loop Optimization |
| title_full_unstemmed | Concurrent Adaptive Control for a Robotic Leg Prosthesis via a Neuromuscular-Force-Based Impedance Method and Human-in-the-Loop Optimization |
| title_short | Concurrent Adaptive Control for a Robotic Leg Prosthesis via a Neuromuscular-Force-Based Impedance Method and Human-in-the-Loop Optimization |
| title_sort | concurrent adaptive control for a robotic leg prosthesis via a neuromuscular force based impedance method and human in the loop optimization |
| topic | robotic leg prosthesis multi-task walking concurrent adaptive control human-in-the-loop optimization |
| url | https://www.mdpi.com/2076-3417/15/15/8126 |
| work_keys_str_mv | AT mingpi concurrentadaptivecontrolforaroboticlegprosthesisviaaneuromuscularforcebasedimpedancemethodandhumanintheloopoptimization |