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机器人·控制
12
engines
正运动学 · 二连杆机械臂
Forward kinematics · 2-link arm
x=L1c1+L2c12 · 2 连杆末端位姿 · 可达工作空间环
Joint angles → end-effector position, computed exactly
逆运动学 · 二连杆机械臂
Inverse kinematics · 2-link arm
余弦定理解 θ · 肘上/肘下两解 · 不可达判定
Target position → joint angles, both elbow configurations
机械臂雅可比 · 速度
Manipulator Jacobian · velocity
v=J·q̇ · 末端速度 · 奇异 detJ=L1L2sinθ2=0
Joint velocities → end-effector velocity; watch the singularity
Gear train ratio
Gear train ratio
比=从动/主动齿数 · 转速反比扭矩正比 · 多级相乘
Drag the gear count and teeth: overall ratio, output speed & torque, and rotation direction update live
Servo PWM control
Servo PWM control
脉宽 1.0–2.0ms→0–180° · 50Hz 帧 · 占空比
Drag the pulse width or the target angle: horn angle, PWM waveform and duty cycle update live
Stepper motor basics
Stepper motor basics
步距角 360/步数 · 1.8°→200/rev · 微步 16×→3200
Pick the step angle, microstepping and step frequency: effective step angle, steps/rev and rpm update live
PID 控制器 · 阶跃响应
PID controller · step response
u=Kp·e+Ki·∫e+Kd·ė · 阶跃响应 · 超调/稳态误差/调节
Deterministic closed-loop simulation of a mass–spring–damper plant
负反馈控制回路
Negative feedback loop
闭环 G/(1+GH) · 扰动抑制 1/(1+GH) · 鲁棒性
Closed-loop gain, robustness and disturbance rejection
梯形速度运动轨迹
Trapezoidal motion trajectory
加速-匀速-减速 · 位置/速度/加速度剖面 · 三角退化
Accelerate to cruise velocity, cruise, decelerate to rest
Differential-drive robot
Differential-drive robot
v=(vr+vl)/2 · ω=(vr−vl)/L · 转弯半径 · 原地转
Two driven wheels set linear speed v, angular speed ω and turn radius R
Wheel odometry (dead reckoning)
Wheel odometry (dead reckoning)
编码器增量航迹推算 x,y,θ · 累积漂移
Integrate encoder increments to estimate pose (x, y, θ) — and watch it drift
Mechanism DOF (Grübler / Kutzbach)
Mechanism DOF (Grübler / Kutzbach)
Grübler 3(n−1)−2j · 机构/结构 · 四连杆 DOF=1
Count links and joints to get mobility — structure, mechanism, or over-constrained