An inverse kinematics function of a manipulator is normally required for the control if its tip. It provides manipulator configurations that allow the manipulator tip to reach desired positions. The configuration, depending on the manipulator structure can be, for example, its joint angles, segment lengths or input pressures.
Since forward kinematics analysis for a continuous, soft robot is quite complicated, the task of determining the inverse kinematics function is also complex. One of the possible ways of resolving this issue is an analytical approach using the constant curvature manipulator model, which provides a simple solution to the forward kinematics problem.
We would like to introduce another approach, which is based on a physical model of the manipulator, called the Bending Model. This model is based on Euler-Bernoulli beam bending theory and does not assume the module curvature to be constant along its length.
The algorithm takes position and disturbing forces as input, and calculates pressures which guarantees reaching a goal position under these conditions. It can be launched for any number of modules. Since there are a lot of solutions for such issue, the algorithm finds the nearest one in the solution space. There is a possibility, that the algorithm will not find the solution even if one exists. That is because, local minimum can occur. The inverse kinematics algorithm is able to keep the tip at the desired position under changing environmental conditions. Figure 21 shows its behavior when an increasing force is applied between second and third segment.
Inverse Kinematics behaviour in respect of changing force value