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先の記事に書いて、シミュレーションで暫定的に動かしてみた座標の設定には、問題があった。
正面図と側面図を同時に書くと上記図のようになる。前回の問題は、ロボットの原点で座標が固定されていなかったことだ。原点の軸においては、回転していなくした。そこで固定して、実際の動きは、それぞれの位置をグローバル座標に変換して表示させるようにすべきだということ。
図はまた、角度の正の向きを定義している。単なる定義であって、定義を変えると途中の式の形は変わるが、結果に変化はない。
原点の座標を
として
の各座標を示そう。ただし、
は、座標これらの座標に直接関係せず、ただ、足の向きを規定しているだけなので、ここでは省略する。
《正面図》
A点とB点の関係
B点とC点の関係
C点と原点の関係
D点と原点の関係
D点とE点の関係
E点とF点の関係
《側面図》
A点とB点の関係
B点とC点の関係
C点とD点と原点の関係
D点とE点の関係
E点とF点の関係
正面図と側面図の
軸の座標は一致しなければならないので、式的には
と
で調整されることになるだろう。つまり、実際の足の長さ、
と与えられた角度から、
の全てが計算できるはずだ。次回はそれを考えてみる。