Inspired by bat flight performance, we explore the advantages of wing twist and fold for flapping wing robots. For this purpose, we develop a dynamical model that incorporates these two degrees of freedom to the wing. The twist is assumed to be linearly-increasing along the wing, while the wing fold is modeled as a relative rotation of the handwing with respect to the armwing. An optimization scheme parameterizes the wing kinematics for 2, 5 and 8 m/s forward flight velocities. The intricate interplay between wing orientation, effective angle of attack and the ensuing lift and thrust generation are discussed. The results show that wing twist and fold alleviate negative lift and thrust in the upstroke, and in some cases producing persistent positive thrust throughout cycle for handwing. As a result, power consumption drops precipitously compared to the base case of a rigid flat plate. Another crucial realization is the relative importance of wing twist and fold in achieving efficient flight strongly depends on speeds. At slow flight, twist is significantly more effective in minimizing the power, but becomes energetically inefficient for fast speeds. The results also show that a 45° wing fold during upstroke is energetically beneficial for all speeds. The synergy of wing twist and fold are most prominent at slow flight. These findings provides useful guidelines for designing flapping wing robots.

We study the dynamics of hovering mechanisms inspired by hummingbirds and bats to extract practical guidelines for the design and control of aerial robots. Using a dynamical model that incorporates wing flapping, pronation and folding, we determine the parameters for which hovering is possible. We show that the pronation angle (rotational degree of freedom for the wing about its span) significantly effects energy consumption of the system and demonstrate an optimal wing-beat frequency that minimizes the average power consumption. Furthermore, we show that increased body rotational inertia can significantly increase the energy consumption of hovering and can lead to implausible hovering trajectories. Last, we show that a bat-inspired hovering mechanism that allows for wing folding can generate plausible hovering behavior for larger aerial systems.

In this paper we propose the fastest converging control policy (also known as deadbeat control) for walking with the bipedal spring-mass model, which serves as an abstraction of a robot on compliant legs. To fully leverage the passive dynamics of the system, the touchdown angle of the swing-leg is assigned as the only control input of the system. We show that two steps (or one stride) are necessary and sufficient to converge to target walking gaits. We first analyze the dynamics of the system to identify the limit cycles as well as the limitations of the control authority within the definition of walking. Then, we present the two-step deadbeat control policy that guarantees stability with the fastest possible convergence rate for the system. For each equilibrium gait, the basin of attraction in which this two-step control exists is a measure of the robustness of the system. The simulation results show that human-like walking gaits (double hump ground reaction force profile) have relatively large basins of attraction. Finally, we extend the policy to various energy levels to accommodate walking on uneven ground that has height changes. We show in simulation that the system indeed rejects various disturbances and converges to the desired equilibrium gait in two steps.

In this paper, we present a novel control strategy for running of bipedal robots with compliant legs. To achieve this goal and to take advantage of the characteristics of the template, we match the dynamics of the full multibody model of a real biped robot with the dynamics of a well-known running template called spring loaded inverted pendulum (SLIP) model. This can be viewed as a template and anchor approach. Because the SLIP model is theoretically conservative, it always operates at a constant energy level. However, real robots operate at various energy levels due to the positive and/or negative work done by the motors, inherent damping/friction of the components and more importantly, the regular ground impact that occurs during the running process. As a case study the proposed controller was implemented on a simulation of the bipedal robot called ATRIAS. The full dynamic equations for running of the ATRIAS robot are derived using the Lagrangian approach. To make our multibody biped robot run with a steady and stable gait that tracks the SLIP model dynamics, a two-level controller is proposed. The upper level controller in stance phase is designed with feedback linearization to make the active SLIP model follow the SLIP model trajectory. The lower level controller in stance phase is designed for the multibody model to track the toe force profile of the active SLIP model. Two active SLIP architectures are proposed for locked and unlocked torso cases of the robot. Simulation results demonstrate stable running based on this strategy for both cases of the ATRIAS model with locked and unlocked torso angle. Matching the SLIP dynamics on running biped robots not designed for spring-mass gaits is impossible due to actuator limitations, or, at best, inefficient.

The passive dynamics of actuators may impose serious limitations to the performance of a system. Existence of inertia for example makes it impossible for the actuators to react immediately. A throwing mechanism (with electric motors) is composed of two inertias (object and motor) that decreases the performance of the system and can not be overcome with software control. But, we can use other elements (like a spring) to make the motor inertia a benefit to improve the performance of the system. Moreover, when the object is directly connected to the motor, the maximum velocity that the object can achieve is limited to the maximum velocity that can be provided by the motor. Previous research shows that passive dynamics is not always harmful, and can increase the performance of a mechanism. Here, we will extract mathematical formula that gives us the required optimum value for stiffness and/or damping of the system to give us the optimal performance given physical limitations.