We present a multi-query recovery policy for a hybrid system with goal limit cycle. The sample trajectories and the hybrid limit cycle of the dynamical system are stabilized using locally valid Time Varying LQR controller policies which probabilistically cover a bounded region of state space. The original LQR Tree algorithm builds such trees for non-linear static and non-hybrid systems like a pendulum or a cart-pole. We leverage the idea of LQR trees to plan with a continuous control set, unlike methods that rely on discretization like dynamic programming to plan for hybrid dynamical systems where it is hard to capture the exact event of discrete transition. We test the algorithm on a compass gait model by stabilizing a dynamic walking hybrid limit cycle with point foot contact from random initial conditions. We show results from the simulation where the system comes back to a stable behavior with initial position or velocity perturbation and noise.

Water strider insects have attracted many researchers' attention with their power efficient and agile water surface locomotion. This study proposes a new water strider insect inspired robot, called STRIDE II, which uses new circular footpads for high lift, stability, payload capability, and a new elliptical leg rotation mechanism for more efficient water surface propulsion. The lift, drag and propulsion forces and the energy efficiency of this robot are modeled and experiments are conducted to verify these models. A maximum lift capacity of 53 grams is achieved with a total of 12 footpads, each 4.2 cm in diameter for a robot weighing 21.75 grams. For this robot, a propulsion efficiency of 22.3% is measured. Maximum forward and turning speeds of the robot are measured as 71.5 mm/sec and 0.21 rad/sec, respectively. These water strider robots could be used in water surface monitoring, cleaning, and analysis in lakes, dams, rivers and sea.