Andrew W. Long

Northwestern University, Evanston, Illinois, United States

Are you Andrew W. Long?

Claim your profile

Publications (4)2.43 Total impact

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: 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.
    Full-text · Article · Jun 2014 · IEEE Transactions on Robotics
  • Navid Aghasadeghi · Andrew Long · Timothy Bretl
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, we develop an approach to inverse optimal control for a class of hybrid dynamical system with impacts. As it is usually posed, the problem of inverse optimal control is to find a cost function that is consistent with an observed sequence of decisions, under the assumption that these decisions are optimal. We assume instead that observed decisions are only approximately optimal and find a cost function that minimizes the extent to which these decisions violate first-order necessary conditions for optimality. For the hybrid dynamical system that we consider with a cost function that is a linear combination of known basis functions, this minimization is a convex program. In fact, it reduces to a simple least-squares computation that—unlike most other forms of inverse optimal control—can be solved very efficiently. We apply our approach to a dynamic bipedal climbing robot in simulation, showing that we can recover cost functions from observed trajectories that are consistent with two different modes of locomotion.
    No preview · Article · May 2012 · Proceedings - IEEE International Conference on Robotics and Automation
  • Source
    A W Long · R D Gregg · K M Lynch
    [Show abstract] [Hide abstract]
    ABSTRACT: We describe and experimentally validate the Simplest Parkour Model (SPM) for the ParkourBot, a planar dynamic climbing robot equipped with two springy BowLegs. By controlling the leg angles and injected energy at im-pact, the ParkourBot is capable of climbing up and down in a rigid chute on an inclined air table. The SPM consists of a point mass and two massless legs. The legs are assumed to be infinitely stiff, resulting in an instantaneous stance phase and a closed-form solution of the hybrid dynamics. In this paper, we show that the SPM is a good predictor of the actual experimental behavior. Using the SPM we compute the fixed points, stability and basins of attraction of period-1 limit cycles.
    Preview · Article · Jan 2012
  • A.W. Long · T.D. Murphey · K.M. Lynch
    [Show abstract] [Hide abstract]
    ABSTRACT: 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.
    No preview · Conference Paper · Jun 2011