We study the design of robust and agile controllers for hybrid underactuated systems. Our approach breaks down the task of creating a stabilizing controller into: 1) learning a mapping that is invariant under optimal control, and 2) driving the actuated coordinates to the output of that mapping. This approach, termed Zero Dynamics Policies, exploits the structure of underactuation by restricting the inputs of the target mapping to the subset of degrees of freedom that cannot be directly actuated, thereby achieving significant dimension reduction. Furthermore, we retain the stability and constraint satisfaction of optimal control while reducing the online computational overhead. We prove that controllers of this type stabilize hybrid underactuated systems and experimentally validate our approach on the 3D hopping platform, ARCHER. Over the course of 3000 hops the proposed framework demonstrates robust agility, maintaining stable hopping while rejecting disturbances on rough terrain.

Robotic hopping requires high performance and precision, due to its extreme interactions with the environment. Designing a system that will perform optimally, or even stably, for this motion primitive is a significant challenge. In previous work, it was shown that designing a robot with two springs (one in series and one in parallel with the actuator) could dramatically improve performance. However, selecting these springs was an intricate process since their dynamics were tightly coupled, and accomplished through trial and error. This work presents a general optimization framework for interconnected systems that designs the time-based hopping motion, while also designing the shape of nonlinear springs on the robot to yield efficient hopping. Utilizing this method, hopping motions and spring designs were generated simultaneously and experimentally verified on a novel hopping robot.

Robotic Hopping is challenging from the perspective of both modeling the dynamics as well as the mechanical design due to the short period of ground contact in which to actuate on the world. Previous work has demonstrated stable hopping on a moving-mass robot, wherein a single spring was utilized below the body of the robot. This paper finds that the addition of a spring in parallel to the actuator greatly improves the performance of moving mass hopping robots. This is demonstrated through the design of a novel one-dimensional hopping robot. For this robot, a rigorous trajectory optimization method is developed using hybrid systems models with experimentally tuned parameters. Simulation results are used to study the effects of a parallel spring on energetic efficiency, stability, and hopping effort. We find that the double-spring model had 2.5x better energy efficiency than the single-spring model, and was able to hop using 40% less peak force from the actuator. Furthermore, the double-spring model produces stable hopping without the need for stabilizing controllers. These concepts are demonstrated experimentally on a novel hopping robot, wherein hop heights up to 40cm were achieved with comparable efficiency and stability.

Hopping is a highly dynamic motion requiring precise input over brief moments of ground contact in order to achieve desired performance. While this problem has been approached from multiple perspectives, this work provides a comparative analysis of two robot models. The first model uses an actuator to store energy in a spring and release it during the ground phase, while the second uses an actuator to move an additional mass vertically to generate force on the spring. In the first model, analytic expressions are used to find the desired controllers, while trajectory optimization is used in the latter. Orbital stability of each model under the conditions of uncertain damping and poor estimation of the hop height is examined. To this end, Poincaré analysis is used to give a metric of stability in the presence of different initial conditions and parameter uncertainty. Simulations show that the first model converges quickly to a point near the desired height determined by the amount of uncertain damping present. The second model is less robust to uncertainty, but is be made to converge to a desired height with the addition of PD control around the optimal trajectory. This robustness is improved with different gains in the controller. In experiments performed on hardware for the second model, stability is observed through convergence to a periodic orbit within several hops.

Bipedal robotic running remains a challenging benchmark in the field of control and robotics because of its highly dynamic nature and necessarily underactuated hybrid dynamics. Previous results have achieved bipedal running experimentally with a combination of theoretical results and heuristic application thereof. In particular, formal analysis of the hybrid system stability is given based on a theoretical model, but due to the gap between theoretical concepts and experimental reality, extensive tuning is necessary to achieve experimental success. In this paper, we present a formal approach to bridge this gap, starting from theoretical gait generation to a provably stable control implementation, resulting in bipedal robotic running. We first use a large-scale optimization to generate an energy-efficient running gait, subject to hybrid zero dynamics conditions and feasibility constraints which incorporate practical limitations of the robot model based on physical conditions. The stability of the gait is formally guaranteed in the hybrid system model with an input to state stability (ISS) based control law. This implementation improves the stability under practical control limitations of the system. Finally, the methodology is experimentally realized on the planar spring-legged bipedal robot, DURUS-2D, resulting in sustainable running at 1.75m/s. The paper, therefore, presents a formal method that takes the first step toward bridging the gap between theory and experiment.

This work presents the preliminary experimental validation of a systematic prosthetic control strategy on a custom compliant transfemoral prosthesis with the end result being energy efficient 3-dimension (3D) multi-contact prosthetic walking. In particular, with the goal of capturing essential components of realistic amputee-prosthesis system, a 3D asymmetric hybrid system model is presented - this forms the foundation for formal gait design and control construction. Based on this model, a two-step direct collocation optimization method is utilized to design an energy efficient multi-contact prosthetic gait in 3D. The designed gaits are also subject to various practical constraints such as human-likeness constraints and comfortability constraints. For experimental validation, a 3D capable powered transfemoral prosthetic device is custom built so as to be amendable to realizing the designed 3D prosthetic gaits. Differentiating this device from existing powered prosthesis, compliant components are added to the three joints (two pitch joints and one roll joint) for the purpose of energy saving and human-like behaviors. Combining the presented control methodology and the novel hardware design, the end result is experimentally realized 3D multi-contact prosthetic walking with improved energy efficiency compared to other devices and control methods.