Path planning of robotic hopping and swinging along an ordered sequence of points

Michael G Kean, Purdue University

Abstract

One of the inherent differences between legged robots and animals is the ability to follow dynamic paths through complicated, unstructured environments when steady state motion is not an option. An approach to traversing the environment in this way utilizing hopping and swinging is presented. The approach defines the path of the robot as an ordered sequence of points that must be used as the contact locations between the limb and the environment. Following this dynamic path is reduced to two tasks. While airborne the robot must orient the limb for landing. During contact with the environment the robot must actuate so that when it leaves contact is travels to the next desired landing position. The task of selecting contact locations that are suitable for exploring a complex, unstructured environment is a very difficult one. As a first foray into this field, an approximate planning space will be described. This planning space models the region of space that a hopping robot could reach in a single jump from contact. When selecting a sequence of points to follow through the environment, each new contact location must lie within the planning space for the previous contact location. The main focus of this work is the determination of a path along an ordered sequence of points. Between each pair of points there will be a ballistic flight, the robot will be airborne and subject only to the acceleration of gravity. There are an infinite number of ballistic flights connecting any pair of points. Using kinetic energy as a metric and utilizing logical tests, a single ballistic trajectory will be selected for each pair of contact points. The ballistic flights compose a piecewise path along the sequence of points. At the end of each flight the robot will contact the environment. It must then act against the environment in order to ensure it leaves contact along the next desired ballistic trajectory. In order to ensure that such actuation is possible, a post processing step will apply consistency constraints to the selected trajectories and modify them as necessary. After this post processing, the actuation necessary to orient the limb prior to landing will be determined. Once the trajectories have been fixed, the actuation during contact will be addressed. Two types of contact are considered: swinging and hopping. The dynamics during swinging are those of a pendulum, the rotation of the limb fully describes the motion of the system. Identifying the actuation torque that connect the landing states to the desired liftoff states is sufficient to resolve swinging contact. Hopping contact is treated as a pendulum with the ability to change length. Not only must the actuation torque be found, but the radial actuation force must be determined. A simplified second order ordinary differential equation will be used to model the radial motion during hopping. Due to the nature of the dynamics, the results of hopping contact cannot be analytically expressed. Numerical methods must be employed to calculate the exact actuation necessary during contact. All actuations developed in this approach will be piecewise constant. In this way the complex path through the environment can be converted into a series of time intervals, each of which has constant actuation. Examples of this approach will be given in both planar and spatial environments.

Degree

Ph.D.

Advisors

Cipra, Purdue University.

Subject Area

Mechanical engineering|Robotics

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