Learn Lisp Programming Using MCUS

Part 3—Forward Kinematics in µLisp

- Raul Alvarez

µLisp is a dialect of the Lisp programming language for MCUs with limited RAM. In Part 1, Raul presented µLisp concepts and syntax, and extensions specific to MCUs, and in Part 2, he added extensions by using custom functions. In Part 3 of this article series, he implements a new extension to multiply matrices, and uses µLisp to implement forward kinematics for a mini robotic arm.

In this last part of the series on Lisp programming with microcontrollers, we will use everything we previously learned about µLisp programming. We will compute "forward kinematics" (the process of computing the pose of a robotic arm, based on the angles of its rotating joints), using homogeneous transformations for the three-degrees-of-freedom (3DOF) mini robotic arm presented in Part 2 of this article series [1]. To achieve this, we will implement a matrix multiplication extension to µLisp. Along the way, we will also continue to further explore the Lisp programming language, while we challenge ourselves with math and the fundamental concepts of robotic arm kinematics.

To follow the topics discussed here, you need to be familiar with Arduino and µLisp programming. Please see the first two parts of this article series for information [1, 2]. "Robot kinematics" refers to the relation between the geometry and movement of a robot. It is also desirable to have some background in robot kinematics with the Denavit-Hartenberg convention and homogeneous transformations, so I will give a simple explanation of the basics. The latter, however, is really tangential to the subject of the entire article series.

LISTS AND ARRAYS

Lists are one of the most fundamental data structures in Lisp. In Part 1, I discussed how to create them. Lines 1-2 from Listing 1 are a reminder of two equivalent methods discussed. However, there's a third method of creating lists by "consing" atoms (Lisp primordial objects) with the