Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to induce a low dimensional system, the zero dynamics, that captures the underactuated aspects of a robot's model, without any approximations. To enhance intuition, the relation between physical constraints and virtual constraints is first established. From here, the hybrid zero dynamics of an underactuated bipedal model is developed, and its fundamental role in the design of asymptotically stable walking motions is established. The chapter includes numerous references to robots on which the highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte

Feedback Linearization of Inertially Actuated Jumping Robots

The focus of robotics recently is in automated navigation. It seems that the engineering community has accepted that the discovery of all means of locomotion has been concluded with quad-copters and other similar drones. However, Inertially Actuated Jumping Robots provide a promising new means of locomotion. The difficulty of IAJR is the hybrid nature of the ground contact/flying dynamics. This combined with the complexity of 3-dimensional translation, can make IAJR very complex. In this paper, a Nonlinear Feedback Linearization controller is introduced to provide controllability in this complexity. The controller design is based on invariant sets. By reducing the divergence from the invariant set, a greater response can be achieved. Within the available power of Kashki\u27s Basketball Robot, the controller in this paper was able to achieve the greatest response to date for the Basketball Robot at a maximum jump height of 0.25 meters. Further simulation shows that without restricting physically or electrically available power, the robot can achieve a jump height of 0.6 meters! The design paradigm used on the basketball robot was extend to a tapping robot. The tapping robot achieved a stable average forward velocity of 0.0773 meters/second in simulation and 0.157 meters/second in experimentation

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I this article we developed two nonlinear force controllers based on the sliding mode control theory. We used the detailed mathematical model of a pneumatic system developed in the first part of the paper. The first controller uses the complete model, and exhibit superior performance both in the numerical simulation and experiments, but requires very complex online computation for the control law. The reduced order controller neglects the valve dynamics and the time delay due to connecting tubes. The control law is greatly simplified, and the numerical simulations and experimental verification shows only slightly reduced performances in configurations with relatively short tubes, and at frequencies up to 25 Hz. At higher frequencies or when long connecting tubes are used, the performances are significantly lower than those provided by the full order Sliding Mode Controller.