Date of Award

Fall 2011

Degree Type


Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Electrical & Systems Engineering

First Advisor

Daniel Koditschek


Biologists have proposed a pendulous climbing model, the Full-Goldman (F-G) template, that abstracts remarkable similarities in dynamic wall scaling behavior exhibited by radically different animal species. This thesis presents a progression of work related to dynamic vertical climbing based on that model.

We begin by describing the inspiration, design, implementation of and experimentation with the first dynamical vertical climbing robot. We study numerically a version of the pendulous climbing template dynamically re-scaled for applicability to utilitarian payloads with conventional electronics and actuation, revealing that the incorporation of passive compliance can compensate for an artifact’s poorer power density and scale disadvantages relative to biology. However, the introduction of these dynamical elements raises new concerns about stability regarding both the power stroke and limb coordination that we allay via mathematical analysis. Combining these numerical and analytical insights into a series of design prototypes, we document the correspondence of the various models to the variously scaled platforms and report that our approximately two kilogram platform, DynoClimber, climbs dynamically at vertical speeds up to 1.5 bodylengths per second — in particular, the final 2.6 kg prototype climbs at an average steady state speed of 0.66 m/s against gravity on a carpeted vertical wall, in rough agreement with our various models’ predictions.

We establish whether the success of the robot is inherent to the morphology suggested by the F-G template or, instead, to a fortuitous set of parameter choices during the robot’s design. Thus we examine the effects of (i) actuator dynamics and (ii) lateral force generation on climber stability by investigating a sequence of reduced order variants of the F-G template. We prove analytically that a purely vertical climber is stable for a general class of actuator force functions, and use that result to further simplify our models by allowing the prescription of leg length. We use that simplification to demonstrate that a sprawled posture stabilizes vertical climbing by damping rotational motion during stride transitions. We also notably demonstrate through simulation that a climber’s stability does not depend on the actuation frequency it employs.

Finally, we explore the potential benefits of pendulous dynamical climbing in animals and in robots by examining the stability and power advantages of variously more and less sprawled limb morphologies when driven by conventional motors in contrast with animal-like muscles. For quadratic-in-velocity power output actuation models typical of commercially available electromechanical actuators, our results suggest the new hypothesis that sprawled posture may confer significant energetic advantage. In notable contrast, muscle-powered climbers do not experience an energetic benefit from sprawled posture due to their sufficiently distinct actuator characteristics and operating regimes. These results suggest that the benefits of sprawled posture climbing may be distinctly different depending upon the details of the climber’s sensorimotor endowment. This study also shows that even minimally intelligent foot placement improves stability when compared to the template-derived rigid sprawl.

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