Switching between Limit Cycles in a Model of Running Using Exponentially Stabilizing Discrete Control Lyapunov Function
This addresses the challenge of creating agile and rapid transitions in robotic running, which is incremental as it builds on existing control Lyapunov function methods.
The paper tackles the problem of enabling agile running motions in robots by switching between periodic motions (limit cycles), achieving a demonstration of switching between 5 limit cycles in about 5 steps with speed changes from 2 m/s to 5 m/s.
This paper considers the problem of switching between two periodic motions, also known as limit cycles, to create agile running motions. For each limit cycle, we use a control Lyapunov function to estimate the region of attraction at the apex of the flight phase. We switch controllers at the apex, only if the current state of the robot is within the region of attraction of the subsequent limit cycle. If the intersection between two limit cycles is the null set, then we construct additional limit cycles till we are able to achieve sufficient overlap of the region of attraction between sequential limit cycles. Additionally, we impose an exponential convergence condition on the control Lyapunov function that allows us to rapidly transition between limit cycles. Using the approach we demonstrate switching between 5 limit cycles in about 5 steps with the speed changing from 2 m/s to 5 m/s.