The ParkourBot climbs in a planar reduced-gravity vertical chute by leaping back and forth between the chute's two parallel walls. The ParkourBot is comprised of a body with two springy legs and its controls consist of leg angles at touchdown and the energy stored in them. During flight, the robot stores elastic potential energy in its springy legs and then converts this potential energy in to kinetic energy at touchdown, when it “kicks off” a wall. This paper describes the ParkourBot's mechanical design, modeling, and open-loop climbing experiments. The mechanical design makes use of the BowLeg, previously used for hopping on a flat ground. We introduce two models of the BowLeg ParkourBot: one is based on a nonzero stance duration using the spring-loaded inverted pendulum model, and the other is a simplified model (the simplest parkour model, or SPM) obtained as the leg stiffness approaches infinity and the stance time approaches zero. The SPM approximation provides the advantage of closed-form calculations. Finally, predictions of the models are validated by experiments in open-loop climbing in a reduced-gravity planar environment provided by an air table.

Hybrid dynamical systems with impacts typically have controls that can influence the time of the impact as well as the result of the impact. The leg angle of a hopping robot is an example of an impact control because it can influence when the impact occurs and the direction of the impulse. This paper provides a method for computing an explicit expression for the first derivative of a cost function encoding a desired trajectory. The first derivative can be used with standard optimization algorithms to find the optimal impact controls for motion planning of hybrid dynamical systems with impacts. The resulting derivation is implemented for a simplified model of a dynamic climbing robot.