Maple and MapleSim play a vital role in 3-D biomechanical modeling and stability analysis of bipedal motion - User Case Studies - Maplesoft

User Case Study: Maple and MapleSim play a vital role in 3-D biomechanical modeling and stability analysis of bipedal motion

How would life change if we could use controllers and software programs to dictate the movement of a body part without actually having to move it ourselves? If current research continues to move into those realms, one day this technology could become a reality.

Biomechanics is the science concerned with the internal and external forces acting on the human body, and the effects produced by these forces. A large part of this field today involves using computer software programs to model specific biomechanical movements such as walking, running, jumping, and standing. MapleSim, a product for physical modeling and multidomain simulation, is a significant tool being used in this process.

The Control Systems Lab researchers at the University of Arkansas at Little Rock, directed by Associate Professor Kamran Iqbal, are doing ground-breaking work in this field. Some of their current research deals with musculoskeletal models, where actuators and controllers are used to emulate the motion of real limbs. Dr. Asif Mahmood Mughal completed his PhD in this lab in collaboration with the Rehabilitation Institute of Chicago. He works on biomechanical modeling of human voluntary movements. This requires a detailed understanding of the kinematic and dynamic behavior of bipedal mechanisms in activities such as walking, running, jumping, and standing. Biomechanical models complement physiological studies to analyze and understand human motor functions.

Dr. Mughal’s research focuses on the sit-to-stand maneuver. Its purpose is twofold: to generate 3-D bipedal models for the biomechanical movements in this maneuver by using MapleSim, and to design a controller based upon physiological relevance. The controller for these models emulates the action of the central nervous system (CNS), which issues commands to the muscle actuations. A mathematical modeling framework is used to study and analyze this biomechanical movement.

What is involved?

Sit-to-stand is a common human task, which involves the combination of a musculoskeletal structure integrated with neural control, as well as a myriad of variables. The movement is studied for an 8-segment rigid body model with physiological motor functions.

The actual mechanism to be modeled is very complex with a system in 13 degrees-of-freedom and 7 joints with sagittal and frontal angles. To achieve the desired motion, Mughal needed to determine the applied torques and moments without violating holonomic constraints in the model in the entire maneuver. In addition, he needed to analyze the stability of the system using various criteria, including Lyapunov’s Indirect Method.

How was MapleSim used?

Using MapleSim and Maple™, he rapidly produced a bipedal model to study the sit-to-stand transfer maneuver. By selecting the joints, bodies and frames carefully, it was easy to create biomechanical models. “Manually deriving the analytical equations for a high-order system is very difficult. With MapleSim and Maple, it is very easy to generate biomechanical models,” Mughal points out.

Bipedal Rigid Body Model,
with sagittal plane angles θ1-θ6 and θ9, frontal plane angles φ7-φ8, φ10

He was particularly pleased with the ability to select different coordinate systems by specifying initial conditions in the MapleSim environment. Unlike other modeling packages that can solve in the absolute coordinate system only, MapleSim allows the user to define the coordinates that appear in the generated symbolic equations of motion. These flexibilities of MapleSim provide a variety of application specific modeling schemes. He generated models to study neuro-mechanism deficiencies, muscular coupling and interactions, etc.

The analytical math equations were quickly defined from the model without the need for code generation. Once the equations were complete, they were imported into Maple for stability analysis, using several available methods.

MapleSim’s Connectivity Toolbox for Simulink® product was used to build exact simulation code in the C language. The model was then easily transferred to Simulink® for simulation and further analysis, where it was found that the MATLAB® linearization of Maple’s generated system was stable, using Lyapunov’s Indirect Method.

Human physiological systems better understood

The results of this modeling process provide a better understanding of the human physiological system during the sit-to-stand movement. The gains at different joints show points where increased effort is required in the movement. This process also shows the correlation between different kinematic variables, and their effect on optimizing the voluntary movement.

Center of Mass and Head Position profiles during
sit-to-stand maneuver for 32nd order system

 “In order to obtain an accurate physiological controlled model, it is necessary for optimization criterion to be defined carefully and close to physiological relevance,” said Mughal. This is where MapleSim was critical to the process. “Different performance optimization matrices provide better representation to simulate the movement for various analyses.” These overall design schemes of human motion with physiological relevance is one of the major contribution in bridging a gap between already existed experimental data and mathematical modeling. MapleSim generates equations for kinematic and kinetic variables with ease, which can be employed to formulate a controller design based upon these equations. The following figure shows profiles of center of mass and head position in sit-to-stand maneuver, with equations from MapleSim exported to MATLAB® for further simulation in Simulink®. “This is really a great tool where the power of analytical modeling of Maple environment combines with controller design and simulation capabilities of MATLAB®,” said Mughal.

As the significance of computer modeling and simulation increases in the field of biomechanics, powerful tools become fundamental to the industry’s progress. MapleSim and Maple continue to be more relevant than ever, with their ability to find exceptionally efficient sets of equations for complicated models, resulting in much reduced simulation times, as well as better design, optimization, simulation, and control of complex engineering systems.

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