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Energy Efficient Compliant Actuator Designs:
While robotic systems are able to achieve previously unprecedented agility, robustness and adaptability, they operate with particularly low efficiency. Energy efficient compliant actuation is the missing ingredient and the key enabler of nextgeneration robotic systems: prosthetic devices, exoskeletons, domestic robots, rescue robots. The goal of this project is to develop a computational approach for computeraided design of efficient compliant actuators. This approach will be used to develop a new generation wearable autonomous exoskeleton for human augmentation and targeted biomedical applications.

V. Chalvet and D.J. Braun, Algorithmic Design of Low Power Variable Stiffness Mechanisms, IEEE Transactions on Robotics, vol. 33, no. 6, pp. 1508–1515, Dec. 2017.

V. Chalvet and D.J. Braun, Criterion for the Design of Low Power Variable Stiffness Mechanisms, IEEE Transactions on Robotics, vol. 32, no. 4, pp. 1002–1010, Aug. 2017.

A. Dahiya and D.J. Braun, Efficiently Tuneable PositiveNegative Stiffness Actuator, IEEE International Conference on Robotics and Automation, Singapore, pp. 12351240, May 2017.
Locomotion in Natural and Artificial Systems:
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 developing an impedance controller that is capable of generating autonomous selforganized locomotion. Experiments on an anthropomorphic biped robot demonstrate one implementation of this control approach.

D. J. Braun, J. E. Mitchell, M. Goldfarb, Actuated Dynamic Walking in a SevenLink Biped Robot, IEEE/ASME Transactions on Mechatronics, vol. 17, no.1, pp. 147156, 2012.

D. J. Braun, M. Goldfarb, A Control Approach for Actuated Dynamics Walking in Biped Robots, IEEE Transactions on Robotics, vol. 25, no. 6, pp. 12921303, 2009.
Compliant and VariableImpedance Robotics:
In this research we 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 the system to achieve better performance. Experiments on the stateoftheart variable stiffness DLR HandArm System developed at the German Aerospace Center demonstrate the benefits.

D. J. Braun, F. Petit, F. Huber, S. Haddadin, P. van der Smagt, A. AlbuSchäffer and S. Vijayakumar, Robots Driven by Compliant Actuators: Optimal Control under Actuation Constraints, IEEE Transactions on Robotics, vol. 29, no. 5, pp. 10851101, 2013.

D. J. Braun, M. Howard, and S. Vijayakumar, “Exploiting variable stiffness in explosive movement tasks,” in 2011 Robotics: Science and Systems, (Los Angeles, California, USA), June/July 2011.
Modeling and Simulation of Constrained Dynamical Systems:
Simulation of constrained dynamical systems, modeled with differential algebraic equations (DAEs), is required in many engineering disciplines. However unlike ordinary differential equations (ODEs), that can be effectively integrated with explicit numerical methods (e.g., RungeKutta), integration of DAEs often requires sophisticated implicit integrators enhanced with iterative constraint stabilization. In this research, we developed an explicit numerical integration scheme which is easy to implement and can be used to accurately simulate constrained dynamical systems modeled with differential algebraic equations. The basic assumption during the development of the integration scheme is that the computational environment is nonideal i.e., the numerical solution is error contaminated, such that, neither the kinematic constraints, nor the energytype conservation law, can be exactly satisfied. Using this assumption, a systematic derivation is carried out which resulted in an equation of motion that directly incorporates the correction terms required for precise satisfaction of the kinematic constraints and prevents energy drift along the numerical solution. Importantly, the kinematic constraint correction terms and the energy correction terms are derived to be independent of each other by taking the geometry of the constrained dynamics rigorously into account. This idea enables decoupled constraint and energy correction, which leads to significant improvement in accuracy over long time integrations.

D. J. Braun and M. Goldfarb, Simulation of Constrained Mechanical Systems – Part I: An Equation of Motion, ASME Journal of Applied 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. 3740, pp. 31513160, 2009.
Nonlinear oscillators for Energy Harvesting Applications:
Vibration energy harvesting devices are built to convert kinetic energy into useful electricity. Most of these devices are linear oscillators, capable of large gain amplification at resonant excitation, but have limited bandwidth under more typical, possibly random ambient vibrations. The goal of this project was to develop a nonlinear oscillator for adaptive energy harvesting from lowfrequency natural vibrations. The ambition was to uncover a physical phenomenon for autonomous energy harvesting applications.
Working principle of an oscillatory energy accumulator:

D.J. Braun, A. Sutas and S. Vijayakumar, Selftuning Bistable Parametric Oscillator: Nearoptimal Amplitude Maximization without Model Information, Physical Review E, 95, 012201, 2017.

D.J. Braun, Optimal parametric feedback excitation of nonlinear oscillators, Physical Review Letters, 116, 044102, 2016.