## Smooth Inverse Kinematic Algorithms for Redundant Robots

### Information

• Started: 01/10/2010
• Finished: 26/09/2011

### Description

The inverse kinematics of a robot is the mapping that, given a goal position, calculates a set of
joint positions so as to place the robot’s end effector in the specified goal. As this is a relevant
issue to move the robot, there has been a lot of work about obtaining a fast and robust inverse
kinematic algorithm. In this work we present the main concerns on finding an inverse kinematics
algorithm for a serial redundant manipulator.
We firstly comment on our motivation, the state of the art and set our objectives, to later
briefly expose some necessary concepts. Then the work is divided into two parts: the first
one, describing analytical methods for solving inverse kinematics, and the second one about
control-based methods.
In the analytical methods, we will see how difficult it may be to have a closed analytical form,
in particular for redundant manipulators, and we will try to solve, not always with success, the
inverse kinematics of some robots.
Then we will move into control-based algorithms, which are iterative methods using the Jacobian
matrix of a robot, and we will firstly discuss the concerns of these methods, which mainly are:
• Convergence: Achieving the specified goal from a given starting position.
• Joint limit avoidance: Given the valid interval for each joint, the algorithm should not
give a solution which cannot be reached due to the joints physical limitations.
• Robustness: When a singularity occurs, the algorithm must be capable of not getting stuck
or become chaotic.
• Cost: The time it takes to find a solution.
We will present a survey on the most used existing control-based algorithms. We point out the
drawbacks of each one of them, to later propose a new way of numerically filtering the Jacobian
matrix, and also a new method to avoid step-depending convergence issues, while respecting joint
limits, to have a very smooth and robust algorithm. All these methods have been implemented
using Matlab to solve the inverse kinematics of some robots. The results of two of them, a 4R
planar robot and the Barrett’s WAM arm, are shown so as to draw conclusions.
To end up, we discuss the convergence of these methods, and the global use of them. The algo-
rithm we propose has the advantadge of successfully respecting joint limits and its convergence
is not being step-dependent makes it more robust. Nevertheless, we also discuss the need of,
when the goal is far from the starting position, add path planning methods to approach the
target.

The work is under the scope of the following projects:

• SGR ROBÒTICA: Grup de recerca consolidat - ROBÒTICA (web)
• GARNICS: Gardening with a cognitive system (web)
• APREN: Modelos perceptivos y técnicas de aprendizaje para robots de servicios (web)
• IntellAct: Intelligent observation and execution of Actions and manipulations (web)