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SimSect: A Hybrid Dynamical System Simulation Tool

SimSect is a general purpose hybrid dynamical system simulation tool, initially motivated by the need to have a working simulation of the compliant hexapod platform. Its logical structure closely parallels that of an earlier hybrid version of DsTool. SimSect provides a convenient framework for the definition and simulation of various hybrid dynamical systems, abstracted from the details of how the discrete time integration works. Some of the key features of SimSect are

  • Support for hybrid dynamical systems, consisting of many different vector fields over different parts of the state space.
  • Accurate detection of transitions between different vector fields by iterative integration near transitions.
  • Visualization of the simulation through a concurrent interface to Geomview, a 3D visualization package.
  • Clear separation of the integration engine from the dynamical model, which can easily be redefined or modified.
  • Designed to be used as a batch simulation tool, with configuration through simple text files and an ascii data file output.

SimSect has been created by Uluc Saranli in The University of Michigan and has been used in the simulation of the compliant hexapod model as well as a planar spring loaded inverted pendulum(SLIP) and a planar ankle-knee-hip(AKH) leg model. There are plans for its redesign and reimplementation to make it a generic framework for the analysis of dynamical systems.

The Simplified Hexapod Model

An important part of our design process is a simplified hexapod model, which we investigate through simulations.

Our simple hexapod model consists of a rigid body with six massless compliant legs. Each leg has three spherical degrees of freedom in the body frame. The radial and the lateral angular degrees of freedom are connected to a passive spring and damper. The forward rotation of the leg is accomplished by a torque actuated motor.

At any instant, each leg can either be touching the ground in stance phase, or be in flight phase where it does not have contact with the ground. As a function of their state as well as phase, legs exert forces and torques on the body, which determine the overall behavior of the system.

A more detailed description of the system, together with derivations of the equations of motion, augmentation of the system with actuator and battery models can be found in the corresponding technical report.


 Forward walking on flat terrain
 Recovery from different initial conditions
 Climbing hills

Created by Uluc Saranli, 1999