# Research

The Braun Lab for Advanced Robotics and Control conducts research in the following areas:

**Superhuman Augmentation using Variable Stiffness Technology****Novel Compliant Actuators for Robots & Humans****Data-driven Optimal Control of Robots****Reverse-Engineering Nature for Locomotion Control in Robots and Humans****Numerical Modeling, Simulation and Control of Robots**

**Superhuman Augmentation using Variable Stiffness Technology**

The goal of this research is to enable human performance augmentation – **without external energy**. In this lab we develop a special type of spring that can change stiffness, i.e a **variable stiffness spring**, to enable human limbs to **supply more energy and exert greater forces **to complete a task, for example running faster or jumping higher.

Augmenting human performance without external energy is not new, and historically has been achieved using the bicycle, which doubles human movement speed while not requiring any batteries. A bicycle does this by using the wheels to passively support the body weight, and using pedals to allow the human to supply energy continuously instead of only when the legs touch the ground. **Variable stiffness springs can also achieve the same results** **as they can passively exert high forces against the ground to support body weight, while allowing the legs to supply energy without touching the ground by compressing the spring in the air.**

Using this similar functionality**, one can effectively run 50% faster without using batteries:**

A. Sutrisno and **D. J. Braun**, How to Run 50% Faster without External Energy, *Science Advances*, 2020.

or make a “vertical bicycle” to jump 3 meters high,** increasing jump height without external energy.**

**Theoretical model of a Variable Stiffness Spring being used to augment jump height.** A. Sutrisno and **D.J. Braun**, Enhancing Mobility with Quasi-passive Variable Stiffness Exoskeletons, *IEEE Transactions on Neural Systems & Rehabilitation Engineering*, 2019.

**Example of exoskeleton with a variable stiffness spring applied to the knee joint.** HF, Lau, A. Sutrisno, TH Chong, and **D.J. Braun**, Stiffness Modulator: A Novel Actuator for Human Augmentation, *International Conference on Robotics and Automation*, 2018.

**Theoretical framework for minimizing energy cost of variable stiffness spring actuators. **

**D.J. Braun**, V. Chalvet, Chong T.-H., S.S. Apte and N. Hogan, **Variable Stiffness Spring Actuators for Low Energy Cost Stiffness Modulation**, IEEE Transactions on Robotics, 2019.

**Novel Compliant Actuators for Robots & Humans**

The goal of this research is to develop an actuator that is able to exert force to complete required tasks – using as little energy as possible. This is done by designing an actuator that consists of a motor attached to compliant elements capable of storing energy. Using compliant elements to exert force minimizes the force the motor must exerts, and therefore the energy supply the actuator consumes. Also, using compliant elements allows one to recycle energy when redirecting velocity, instead of dissipating velocity before supplying energy to accelerate.

Often in certain tasks the force required to complete the task does not do any net mechanical work, eg. supporting a weight against gravity. Therefore, it would be more efficient to use compliant elements to exert force to perform parts of the task that are zero net mechanical work, e.g redirecting velocities, deceleration, while leaving the motor to exert force only when the system requires net mechanical work.

Human locomotion is a good example of a task that consists of zero net mechanical work (supporting body weight, swinging legs back and forth), and nonzero net mechanical work (horizontal acceleration in walking/running) tasks.

**Example of a compliant actuator (motor + springs) being used to control a robot leg. **

**D.J. Braun**, V. Chalvet and A. Dahiya, **Positive-Negative Stiffness Actuators**, *IEEE Transactions on Robotics*, 2018.

**Data-driven Optimal Control of Robots**

Optimal control provides a systematic approach to control robots. However, optimal controllers computed using inexact model information lead to significant performance degradation. One way to avoid this limitation is to completely discard model information. However, model-free optimal control approaches are computationally expensive (even inexact models can significantly speed up the optimal control computation).

In this lab we develop algorithms employing a** novel data-driven optimal control formulation that uses inexact models to speed up the computation, while at the same time avoids significant performance degradation due to the use of inexact model information. **Experiments on a three link direct drive torque controlled robot demonstrate the benefits of one such hardware-in-the-loop optimal control method (see Chen and Braun, *IEEE TRO*, 2019).

Y. Chen and **D.J. Braun**, Hardware-in-the-Loop Iterative Optimal Feedback Control without Model-based Future Prediction, *IEEE Transactions on Robotics*, 2019.

Using optimal control, we also investigate **how impedance control strategies emerge from first principles of optimality, and how these strategies can be applied to variable impedance actuation.** We utilize *computational optimal control* to devise controllers that exploit the intrinsic compliance and the natural dynamics of robots to achieve better performance. Experiments on the **DLR Hand-Arm System developed at the German Aerospace Center** demonstrate the benefits.

**D.J. Braun**, F. Petit, F. Huber, S. Haddadin, P. van der Smagt, A. Albu-Schaffer and S. Vijayakumar, Robots Driven by Compliant Actuators: Optimal Control under Actuation Constraints, IEEE Transactions on Robotics, 2013.

**Reverse-Engineering Nature for Locomotion Control in Robots and Humans**

The goal of this research is to discover the *physical reasons* and control principles that govern movements of humans and animals and to utilize these findings to *build next generation robotic devices*. We have focused on the control aspect of this problem by (1) developing an *impedance controller* that is capable of generating *autonomous self-organized locomotion, *(2) extracting controllers form experimental data consistent with human locomotion, (3) developing physics base simulation tools to predict the motion of robot locomotion, (4) developing optimization based constrained impedance controllers that simultaneously provide cyclic limb coordination and upper body stabilization during the inherently unstable task of bipedal locomotion.

Numerical simulations and experiments on an *anthropomorphic biped robot* demonstrate some of these ideas.

**D.J. Braun**, Jason E. Mitchell and M. Goldfarb, Actuated Dynamic Walking in a Seven-Link Biped Robot, *IEEE/ASME Transactions on Mechatronics*, vol. 17, no.1, pp. 147-156, 2012.

E.S. Altinkaynak and **D.J. Braun**, A Phase-Invariant Linear Torque-Angle-Velocity Relation Hidden in the Human Walking Data, IEEE Transactions on Neural Systems & Rehabilitation Engineering, 2019.

L. Li and **D.J. Braun**, **Constrained Feedback Control by Prioritized Multi-objective Optimization**, IEEE International Conference on Robotics and Automation, 2019.

**D.J. Braun**, M. Goldfarb, **A Control Approach for Actuated Dynamics Walking in Biped Robots**,* IEEE Transactions on Robotics*, 2009.

**Numerical Modeling, Simulation and Control of Robots**

We conduct physics-based simulation and optimization-based control of walking robots treated as constrained dynamical systems that interact with their environment.

Y. Li, H. Yu, and **D.J. Braun**, **Algorithmic Resolution of Multiple Impacts in Non-smooth Mechanical Systems with Switching Constraints**, IEEE International Conference on Robotics and Automation, 2019.

Simulation of constrained dynamical systems, modeled with *differential algebraic equations (DAEs),* are required in many engineering disciplines. However unlike ordinary differential equations (ODEs), that can be effectively integrated with explicit numerical methods (e.g., Runge-Kutta),* integration of DAEs often requires sophisticated implicit integrators enhanced with iterative constraint stabilization.*

In this lab we develop numerical methods to derive modified equation of motions that directly incorporate correction terms required for precise satisfaction of the kinematic constraints. This significantly reduces the energy drift over time in the simulated numerical solution.

**D. J. Braun** and M. Goldfarb, Simulation of Constrained Mechanical Systems – Part I: An Equation of Motion, *ASME Journal of Appli**ed** Mechanics*, vol. 79, issue 4, 041017, 2012.

**D. J. Braun**, M. Goldfarb, Elimination of Constrained Drift in the Numerical Simulation of Constrained Dynamical Systems, *Computer Methods in Applied Mechanics and Engineering*, vol. 198, no. 37-40, pp. 3151-3160, 2009.