# HEiKA-EXO: Optimization-based development and control of an exoskeleton for medical applications

**Katja Mombaur, Henning Koch - IWR**

Tamim Asfour - KIT

This project, which was financed by the HEIKA joint research initiative of the University of Heidelberg and the KIT from Jan. to Dec. 2013 was a short prototype study for the design and control of a lower leg exoskeleton for medical applications. Exoskeletons are orthoses that cover all or at least a big part of the body human body, and can also be described as robotics suits or wearable robots. The first exoskeletons became available around 2005 and were destined to make healthy people walk faster or further and to carry large loads, e.g. for nurses in hospitals or for soldiers, amplifying the muscle forces produced by humans. Latest developments have allowed to generate enough energy on board to produce exoskeleton movement without any or just little muscular support by the human. This makes exoskeletons interesting for medical applications. e.g. to allow paraplegic patients or patients which are seriously affected by multiple sclerosis in the lower limb - who would otherwise be bound to wheelchairs - to walk again.

The control of such a combined human-robot system is a challenging task. With respect to stand-alone autonomous robots, it has the advantage of the availability of human intelligence in the system and of human reflexes in at least part of the body. On the other hand, the robotics part, i.e. the exoskeleton, must exhibit a sufficient robustness to also cope with unforeseen control inputs and perturbations from the human user. A lot of progress has been made in the field of powered exoskeletons, but many issues are still unsolved, and it is still a quite a far way to go until paraplegic patients will be able to walk autonomously with exoskeletons without additional crutches, and without quickly fatiguing.

The aim of this prototype study wass to address some of these issues by the combined expertise available at KIT in humanoid robotics including mechatronics design, motor control, multimodal perception (vision, force, tactile) and system integration and the Unversity of Heidelberg in mathematical modeling, simulation and optimization of human and humanoid movements The aim was to develop basic exoskeleton technologies and a first prototype as well as control approaches for combined human-robotic systems on the basis of the ARMAR humanoid robot technologies of KIT and model-based optimization techniques for design and control.

This webpage shortly summarizes the modeling and optimization work in the project done at the University of Heidelberg.

**Modeling and optimization tools to support the exoskeleton design and analyze combined human-exoskeleton motions **

In this part of the project, we have developed a highly flexible, modular and extensible framework which can simultaneously optimize the design of the exoskeleton and the combined human-exoskeleton motions. The resulting human-exoskeleton model is fully parametrized, which means that

a. the model can be adjusted to persons / patients of different sizes and shapes by adjusting the corresponding parameters of the human model. These parameters are then kept constant for the computations performed for this particular person.

b. The parameters in the exoskeleton part of the model are free to be altered by the optimization solver allowing to modify its kinematic and dyanmic properties of the design.

First optimal control problems (due to time constraints) have been formulated for walking problems. The setup is based on the parameterized Human-Exoskeleton model to validate the concept of this approach and assess the potential of further investigations. First results and conclusions will be presented below.

**Modeling**

The generic exoskeleton model shown in Figure 3 consists of 13 distinct components, 6 frames for each leg and a common pelvic traverse. All frames are generically built in a first approximation from an assembly of geometric primitives to allow for a simple design parameterization. These frames are connected by 12 rotatory degrees of freedom – 3 at each hip, 1 at each knee and 2 at each ankle joint (see figure 3 for details).

The human model consists of 3 segments for each leg, 2 segments for each arm (hands are rigidly connected to the Radius segment), 2 torso elements and a head with a total of 32 degrees of freedom. Dynamic characteristics are based on the data set from Paolo de Leva for young female and male adults (gender is chosen during model build process) and parameterized with respect to total body mass and body length. While the dynamic characteristics compare reasonably to other scientific human data sets (e.g. Dumas) some geometric specifications (at the foot) were decided to be not sufficiently accurate. For an authentic modeling of walking locomotion for concept-studies a new foot model was proposed and integrated into the model. In order to individually adapt to patients further dispatched scaling of each body segment with respect to length, mass and density in addition to de Leva's scale parameters is possible. The current generic Exoskeleton design follows the general segmentation strategy of the human models, but with a separated materials density parameter and the implementation of technical joint realizations.

For efficient modeling a new and now already well tested dynamic model package (DYNAMOD) has been established that merges the ideas of symbolic modeling (implemented in the dynamic package HuMAnS) with the 6D spatial algebra formalism of Roy Featherstone. It produces fully parameterizable arithmetic expressions in C-Code that are further exploitable e.g. for highly accurate automatic differentiation (see TAPENADE, ADOL-C). The model-definition is based on Lua and compatible to other resources developed in the ORB research group for verification and 3D visualization. Besides dynamic computations the software provides further 6D dynamic and kinematic model information for complex contact modeling, internal stress and stability analysis.

**Optimization**

The walking motion is modeled as half cycle with 4 distinct phases and changes in the contact constraints during phase-transitions implicitly determined by the underlying motion physics (see Figure 2 for details). The whole body dynamics are represented as hybrid forward dynamic model. The optimal control problem is then formulated as pure quadratic motion fit with subject to the hybrid model dynamics, the boundary (symmetric periodicity/implicit phase switches) as well as continues path constraints.

The problem is then solved with the powerful framework MUSCOD II which is based on a direct multiple shooting approach. It applies a discretization of the controls on an equally distributed time grid along with the system states to transform the boundary value problem into a series of initial value problems. The resulting non-linear program is then solved efficiently using specifically tailored SQP-methods.

Motion trajectory objective as joint angles and model parameters are directly obtained from Vicon Nexus Motion Capturing data and remapped on the configured Human-Exoskeleton model. As the human-exoskeleton model kinematics and dynamics are substantially different from a real human performing a normal walk, one can observe a considerable deviation (walking velocity, phase times, step locations) between the objective and the finally converged motion. At one hand this error may come from an over-restrictive modeling and at the other from the intrinsic kinematic and dynamic characteristics of the model to be analyzed carefully. For conception the resulting joint trajectory and joint velocity profiles as well as peaks in the joint torques structural stress are of high interest. For the most interesting joints (e.g. knee/ankle) we could observe peak-torques and stresses over 100Nm and high discontinuities and peak-velocity around 17RAD/s, an information that will be absolutely essential to the reliability of the mechanical conception and the actuation system of the device.

In the future this setup will be used to analyze the different weight distributions, limitations on the mechanical structure and the actuation system as well as different control algorithms to support the development and construction with essential information to assure reliable operation of the resulting prototype.

### Publications:

- K. H. Koch, K. Mombaur - [Abstract, Poster] ExOpt - A tool for evaluating Exoskeleton designs using Model-based optimization. In International Workshop on Wearable Robots (WeRob), Spain, Parador de Baiona, 2014