33 research outputs found
Averaged Anchoring of Decoupled Templates in a Tail-Energized Monoped
We refine and advance a notion of parallel composition to achieve for the first time a stability proof and empirical demonstration of a steady-state gait on a highly coupled 3DOF legged platform controlled by two simple (decoupled) feedback laws that provably stabilize in isolation two simple 1DOF mechanical subsystems. Specifically, we stabilize a limit cycle on a tailed monoped to excite sustained sagittal plane translational hopping energized by tail-pumping during stance. The constituent subsystems for which the controllers are nominally designed are: (i) a purely vertical bouncing mass (controlled by injecting energy into its springy shaft); and (ii) a purely tangential rimless wheel (controlled by adjusting the inter-spoke stepping angle).We introduce the use of averaging methods in legged locomotion to prove that this âparallel compositionâ of independent 1DOF controllers achieves an asymptotically stable closed-loop hybrid limit cycle for a dynamical system that approximates the 3DOF stance mechanics of our physical tailed monoped.We present experimental data demonstrating stability and close agreement between the motion of the physical hopping machine and numerical simulations of the (mathematically tractable) approximating model.
More information: http://kodlab.seas.upenn.edu/Avik/AveragingTSLI
The Penn Jerboa: A Platform for Exploring Parallel Composition of Templates
We have built a 12DOF, passive-compliant legged, tailed biped actuated by
four brushless DC motors. We anticipate that this machine will achieve varied
modes of quasistatic and dynamic balance, enabling a broad range of locomotion
tasks including sitting, standing, walking, hopping, running, turning, leaping,
and more. Achieving this diversity of behavior with a single under-actuated
body, requires a correspondingly diverse array of controllers, motivating our
interest in compositional techniques that promote mixing and reuse of a
relatively few base constituents to achieve a combinatorially growing array of
available choices. Here we report on the development of one important example
of such a behavioral programming method, the construction of a novel monopedal
sagittal plane hopping gait through parallel composition of four decoupled 1DOF
base controllers.
For this example behavior, the legs are locked in phase and the body is
fastened to a boom to restrict motion to the sagittal plane. The platform's
locomotion is powered by the hip motor that adjusts leg touchdown angle in
flight and balance in stance, along with a tail motor that adjusts body shape
in flight and drives energy into the passive leg shank spring during stance.
The motor control signals arise from the application in parallel of four
simple, completely decoupled 1DOF feedback laws that provably stabilize in
isolation four corresponding 1DOF abstract reference plants. Each of these
abstract 1DOF closed loop dynamics represents some simple but crucial specific
component of the locomotion task at hand. We present a partial proof of
correctness for this parallel composition of template reference systems along
with data from the physical platform suggesting these templates are anchored as
evidenced by the correspondence of their characteristic motions with a suitably
transformed image of traces from the physical platform.Comment: Technical Report to Accompany: A. De and D. Koditschek, "Parallel
composition of templates for tail-energized planar hopping," in 2015 IEEE
International Conference on Robotics and Automation (ICRA), May 2015. v2:
Used plain latex article, correct gap radius and specific force/torque
number
Approximating the Stance Map of a 2-DOF Monoped Runner
We report in this paper a relatively simple means of generating closed-form approximants to the return map associated with a family of nonintegrable Hamiltonian systems. These systems arise in consideration of legged locomotion by animals and robots. The approximations proceed through the iterated application of the mean value theorem for integral operators applied to a nonintegrable perturbation of the system of interest. Both the accuracy of these approximants and their algebraic intractability grow in a relatively controlled manner.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42417/1/332-10-5-533_00100533.pd
Parallel Composition of Templates for Tail-Energized Planar Hopping
We have built a 4DOF tailed monoped that hops along a boom permitting free sagittal plane motion. This underactuated platform is powered by a hip motor that adjusts leg touchdown angle in ïŹight and balance in stance, along with a tail motor that adjusts body shape in ïŹight and drives energy into the passive leg shank spring during stance. The motor control signals arise from the application in parallel of four simple, completely decoupled 1DOF feedback laws that provably stabilize in isolation four corresponding 1DOF abstract reference plants. Each of these abstract 1DOF closedloopdynamicsrepresentssomesimplebutcrucialspeciïŹc component of the locomotion task at hand. We present a partial proof of correctness for this parallel composition of âtemplateâ reference systems along with data from the physical platform suggesting these templates are âanchoredâ as evidenced by the correspondence of their characteristic motions with a suitably transformed image of traces from the physical platform.
For more information: http://kodlab.seas.upenn.edu/Avik/ICRA201
Technical Report on: Tripedal Dynamic Gaits for a Quadruped Robot
A vast number of applications for legged robots entail tasks in complex,
dynamic environments. But these environments put legged robots at high risk for
limb damage. This paper presents an empirical study of fault tolerant dynamic
gaits designed for a quadrupedal robot suffering from a single, known
``missing'' limb. Preliminary data suggests that the featured gait controller
successfully anchors a previously developed planar monopedal hopping template
in the three-legged spatial machine. This compositional approach offers a
useful and generalizable guide to the development of a wider range of tripedal
recovery gaits for damaged quadrupedal machines.Comment: Updated *increased font size on figures 2-6 *added a legend, replaced
text with colors in figure 5a and 6a *made variables representing vectors
boldface in equations 8-10 *expanded on calculations in equations 8-10 by
adding additional lines *added a missing "2" to equation 8 (typo) *added mass
of the robot to tables II and III *increased the width of figures 1 and
An Empirical Investigation of Legged Transitional Maneuvers Leveraging Raibertâs Scissor Algorithm
We empirically investigate the implications of applying Raibertâs Scissor algorithm to the Spring Loaded Inverted Pendulum (SLIP) model in combination with other controllers to achieve transitional maneuvers. Specifically, we are interested in how the conjectured neutral stability of Raibertâs algorithm allows combined controllers to push the systemâs operating point around the state space without needing to expend limited control affordance in overcoming its stability or compensating for its instability. We demonstrate 2 cases where this facilitates the construction of interesting transitional controllers on a physical robot. In the first we use the motors in stance to maximize the rate of change of the body energy; in the second we take advantage of the local environmental energy landscape to push the robotâs operating point to a higher or lower energy level without expending valuable motor affordance. We present data bearing on the energetic performance of these approaches in executing an accelerate-and-leap maneuver on a monopedal hopping robot affixed to a boom in comparison to the cost of anchoring the robot to the SLIP template.
For more information: Kod*la