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This paper introduces an approximate analytical solution to the otherwise non-integrable double-stance dynamics of the bipedal spring-loaded inverted pendulum (SLIP). Despite the apparent structural simplicity of the SLIP, the exact analytical solution to its stance dynamics cannot be found. Approximate maps have been proposed for the monoped SLIP runner (encompassing a single-stance phase). Still,...
Legged robots are intrinsically nonlinear hybrid dynamic systems due to the intermittent contact of the feet with the ground. For optimal performance, in the sense of maximizing speed or energy consumption, different motion control affects the stance from the swing leg during a stride. Designing such controllers, however, can be a daunting task when there is a lack of knowledge about the exact operating...
Various applications in scheduling, such as train timetables and multi-legged locomotion, can be modeled using systems of max-plus linear equations. In this framework, the eigenvalue of the system matrix represents the total cycle time, whereas the eigenvector dictates the steady-state behavior. For a class of concurrent two-state cyclic systems, with direct application to legged locomotion, we present...
Switching gaits in many-legged robots can present challenges due to the combinatorial nature of the gait space. In this paper we present an intrinsically safe gait switching generator that minimizes the velocity variance of all the legs in stance, allowing for smooth acceleration in legged robots. The gait switching generator is modeled as a max-plus linear discrete event system which is translated...
We present an unscented Kalman filter based state estimator for a fast moving rigid body (such as a mobile robot) endowed with two video cameras. We focus on forward velocity estimation towards the computation of standard energy cost functions for legged locomotion. Points are chosen as image features and the model of each camera is based on the traditional pinhole projection. The resulting filter's...
We present a new class of gait generation and control algorithms based on the switching max-plus modeling framework that allows for the synchronization of multiple legs of walking robots. Transitions between stance and swing phases of each leg are modeled as discrete events on a system described by max-plus-linear state equations. Different gaits and gait parameters can be interleaved by using different...
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