Energy-efficient legged locomotion in robots depends on exploiting passive dynamics, particularly with integrated mechanical compliance. Traditional model-based control strategies that leverage these dynamics often encounter challenges due to inherent model uncertainties. We propose a novel model-free method for generating motor trajectories in compliantly actuated monopods using teleoperation with force feedback. This approach allows operators to detect ground reaction forces and excite the robot's natural frequency, achieving highly efficient hopping. The method results in a mechanical Cost of Transport (CoT) of 0.25 at 0.63 m S−1on an articulated hopper. To further enhance energy efficiency and adjust for hardware variations, these trajectories are refined using Black-Box Optimization (BBO) directly on the hardware. Experimental results confirm that these optimized trajectories closely match the efficiency of those initiated by humans, demonstrating the effectiveness of this method in exciting the robot's natural dynamics.

Differential elastic actuators connect a motor and a spring via differential gears to a shared output shaft, offering a more compact solution for creating mechanically robust systems than series elastic actuators, with superior torque transmission at high frequencies. The key to maximizing DEA performance lies in the careful selection of stiffness, inertia, and damping values to meet specific requirements for performance and durability. We introduce a DEA design guide that utilizes open-loop torque-bandwidth for performance evaluation and the magnitude of impact-induced gear torque for robustness evaluation. This approach enables determining DEA parameters using closed-form equations, eliminating the need for simulations or extensive expert knowledge. The effectiveness of our method is confirmed through experiments with a reconfigurable DEA prototype.

Lightweight robots are known to be intrinsically elastic in their joints. The established classical approaches to control such systems are mostly based on motor-side coordinates since the joints are comparatively stiff. However, that inevitably introduces errors in the coordinates that actually matter: the ones on the link side. Here we present a new joint-torque controller that uses feedback of the link-side positions. Passivity during interaction with the environment is formally shown as well as asymptotic stability of the desired equilibrium in the regulation case. The performance of the control approach is experimentally validated on DLR's new generation of lightweight robots, namely the SARA robot, which enables this step from motor-side-based to link-sided-based control due to sensors with higher resolution and improved sampling rate.

We present a new approach for Cartesian impedance control of compliantly actuated robots with possibly nonlinear spring characteristics. It reveals a remarkable stiffness and damping range in the experimental evaluation. The most interesting contribution, is the way the desired closed-loop dynamics is designed. Our control concept allows to add a desired stiffness and damping directly on the end-effector, while leaving the system structure intact. The intrinsic inertial and elastic properties of the system are preserved. This is achieved by introducing new motor coordinates that reflect the desired spring and damper terms. Theoretically, by means of additional motor inertia shaping it is possible to make the end-effector interaction behavior with respect to external loads approach, arbitrarily close, the interaction behavior that is achievable by classical Cartesian impedance control on rigid robots. The physically motivated design approach allows for an intuitive understanding of the resulting closed-loop dynamics. We perform a passivity and stability analysis on the basis of al physically motivated storage and Lyapunov function.

This paper proposes an integration of multi-body and actuator control for multi-contact balancing for robots with highly elastic joints. Inspired by the structure preserving control concept for series-elastic fixed-base robots, the presented approach aims to minimize the control effort by keeping the system structure intact. Balancing on multiple contacts requires to solve the force distribution problem. In locomotion, contacts change quickly, requiring a swift redistribution of contact forces. This is a challenge for elastic robots as the actuator dynamics and limits prevent instantaneous changes of contact forces. The proposed dynamically consistent force distribution is implemented as a model predictive controller which resolves redundancy while complying with contact force and actuator constraints.

Physical compliance can be considered one of the key technical properties a robot should exhibit to increase its mechanical robustness. In addition, the accompanying temporal energy-storing capabilities enable explosive and energy efficient cyclic motions. But these advantages come at a price, as compliance introduces unwanted intrinsic oscillatory dynamics, underactuation, and reduces the natural frequency of the plant. These aspects make control of the link configuration variables a challenging task. This paper presents two novel control methods for implementing link-side motion tracking capabilities and injecting a desired damping characteristic to suppress link vibrations along the reference trajectory for compliantly actuated robots with nonlinear elastic characteristics. We prove their uniform global asymptotic stability by invoking a theorem by Matrosov. Both approaches, namely elastic structure preserving (ESP) and ESP+, have in common that they preserve the link-side inertial properties and the elastic structure of the original plant dynamics, hence the name ESP control. Apart from that, ESP control focuses on preserving the inertial properties of motor dynamics. While ESP+ control aims at minimizing the dynamic shaping on the motor side. The performance of the feedback control laws have been evaluated on the Hand Arm System from the German Aerospace Center (DLR), a variable stiffness robot arm, where the stiffness in each of its joints is highly nonlinear. To the best of our knowledge, this is the first experimentally validated tracking controller for compliantly actuated, multijoint robots with nonlinear elastic elements.

This paper presents a control method to implement trajectory tracking and disturbance rejection characteristics for the link-side dynamics of compliantly actuated robots with nonlinear spring characteristics. This is achieved by introducing new motor coordinates reflecting the damping and feedforward terms and shaping the dynamics of the motor such that it structurally equals the dynamics in the original coordinates. Thus, the approach achieves the control goal while changing the original plant dynamics only to a minimum extent. Passivity, stability, and convergence properties of the closed loop dynamics are proven. The performance of the control approach has been experimentally evaluated on the variable stiffness robot arm DLR Hand Arm System, where the stiffness in each of the joints is highly nonlinear. To our best knowledge, this is the first experimentally validated tracking controller for compliantly actuated robots with nonlinear elastic elements.