自行车机器人动力学建模与MIMO反馈线性化

Dynamic Modeling of Bicycle Robot and Nonlinear Control Based on Feedback Linearization of MIMO Systems

基于拉格朗日方法建立了自行车机器人的多输入多输出动力学模型.为了达到使自行车机器人保持自平衡的目的,将车把转动角度、车体倾倒角度和后轮转动速度作为系统输出;将转动车把的力矩、调节质心的力矩和后轮的驱动力矩作为系统输入,从而构建了具有3个输入、3个输出的仿射非线性系统.基于多输入多输出仿射非线性系统的输入输出线性化理论对其进行分析,通过精确线性化得到了等效的线性系统,并对该等效线性系统进行了分析,通过状态反馈实现了极点配置.通过计算机仿真验证了该控制律的有效性.

A kind of dynamic model of bicycle robot was built based on the lagrange method. To keep bicycle self-balance, the steering angle, the roll-angle and the rear wheel velocity were taken as system outputs; the steering, mass balancing and rear-wheel toque were taken as inputs. Therefore, a multiinput and multi-output （MIMO） affine nonlinear system was constructed. Then input-output linearization control theory was applied to analyze the affine nonlinear system, so that the equal linear system was achieved by exact linearization. By analysis of the equal linear system and state feedback method, the desired pole locations were realized. Computer simulations verified the validity of the control algorithm.