Example of Synthesis of Control Actions for Six-Legged Walking Robot when Moving on ‎Rough Surface

Abstract

Control actions are provided on the basis of inverse kinematic problem. Now there is a set of methods to solve this task.

This article considers an example of the author’s approach application to the inverse kinematic problem.

The main idea of approach is as follows:

1. The limited set of the joints necessary to implement the chosen gait is selected from all joints of the robot. For these joints a strict sequence of the movement within each step and restriction of changing generalized coordinates are specified. 2. The joints non-involved in implementing the chosen gait are disabled, with no calculations performed for them.

Thus, the sources of basic data for the inverse kinematic problem are the kinematic scheme of the executive mechanism of the walking robot and the chosen gait.

To use the offered approach it is necessary:

1. To number the legs and their joints.

2. To choose joints to be involved in realization of the chosen gait.

3. To appoint a sequence of the change of supporting legs when moving by the chosen gait.

4. To specify a motion sequence of the chosen joints within a step for each leg.

5. To specify restrictions of changes of the generalized coordinates in the chosen joints.

The inverse kinematic problem process consists in gradual approach to the solution by change (increase or decrease) of the generalized coordinates in the same order in which the joints of a leg corresponding to these coordinates move within a step by the chosen gait when walking.

Criterion of completing calculations is the limits reached or the fact that a leg is fixed on a supporting plane by a contact sensor (or a condition in the modeling program). Changes of generalized coordinates are within a cycle; each generalized coordinate changes by a certain value at each of iterations of a cycle. The total time of a cycle corresponds to the estimated time of a step to be done.

Advantages of the approach are following: unambiguity of the received solution, possibility to consider degenerate configurations of the executive mechanism of the walking robot, possibility to calculate in the conditions of kinematic redundancy, and high-speed calculations.

The possibility to consider degenerate configurations is owing to the fact that, when calculating, the device of matrix transformations is not used (in particular, calculation of the return matrix of Jacobi).

The possibility to calculate in the conditions of kinematic redundancy, unambiguity of the received solution and high speed are caused by fact that the sequence of the joints movement initially defines a certain desirable leg configuration in space and, in fact, specifies a solution direction.

There is no need to verify the received solution as kinematic restrictions has been are already taken into consideration in the course of calculations.

One more important advantage of the approach is the fact that robots can have any number of legs, and joints in legs.

A lack of possibility to create universal algorithms for the walking robots with essentially different kinematic schemes (for example, anthropomorphous and arachnoid) because of constructive differences in executive mechanisms can be the shortcoming of the approach. But other heuristic methods, such as FABRIK, FTL or CCD also have the same shortcoming. The approach is akin to these methods by the fact that there is no certain formula which use allows us to receive the solution with these methods at once. There are only algorithms of search checking a set of the specified conditions, which are criteria of correction or end of the solution when calculating.