差分方程式拘束を伴う離散時間非ホロノミック系の運動計画

荒井　裕彦

日本ロボット学会誌，Vol. 18, No. 6, pp. 823-830, 2000.

［和文要旨］

　一般化座標の差分方程式として表される拘束を受ける，離散時間非ホロノミック系の概念を導入する．こうした系は連続時間非ホロノミック系のディジタル制御や不連続な拘束条件の反復的変化によって生じる．平行２車輪移動ロボットおよび多面体のピボット操作を例として示す．経由するステップ数に依存するステップ可到達領域を定義し，こうした系の可到達性について考察する．離散時間非ホロノミック系の運動計画問題と冗長マニピュレータの逆運動学問題との類似性に着目し，到達状態の入力列に関するヤコビ行列を用いた運動計画手法を提案する．

Motion Planning of Discrete-time Nonholonomic Systems with Difference-Equation Constraints

Hirohiko Arai

Journal of the Robotics Society of Japan, Vol. 18, No. 6, pp. 823-830, 2000.

[Abstract]

The concept of discrete-time nonholonomic systems, in which the constraints cannot be represented as algebraic equations of generalized coordinates, is introduced. In particular, the constraints formulated as differece equations of generalized coordinates are considered. Such systems can be seen in the digital control of continuous-time nonholonomic systems, and in mechanical systems with repetitive and discontinuous constraints. A two-wheeled mobile robot and pivoting manipulation of a polyhedral object are described as simple examples. The k-step reachable region is defined as the set of the k-th state which the system can reach from the initial state, and the reachability of such systems is discussed. A motion planning method using the Jacobian matrix of the state with regard to the input series is proposed.

[Keywords]

Nonholonomic system, Discrete-time system, Difference equation, Nonlinear system, Step reachability, Motion planning