path planning

• Geometrical description of the robot’s movement in space
• smooth transition between two or more target points
• A unique geometrical path can be described by different time dependent trajectories
• Nomenclature(命名法)
  • PTP
  • Line
  • Circle
  • Splines

1. Point to Point(PTP)

• Linear interpolation of joint axes
• t is just parameter describing the curve from zero to one only geometrically
• no direct control over TCP position and orientation
• they have no control over the actual path of the end effector of the robot
• cyclic call of the kinematic
• time-optimal movement(move as fast as joint axes can)
• only movement that can modify joint configuration

2. path-interpolated movements

• orientation cannot be interpolated linearly when using Euler angle

3. Quaternions

• convenient way to express an orientation
• commutative means that (교환법칙이 성립할 때를 의미함)
• Vs Euler angles
  • unique representation of rotation
  • can be easily interpolated
• Vs Rotation Matrix
  • more compact representation
  • easy to interpolate
  • do not suffer from numerical approximation
• slerp(Spherical Linear interpolation:구면보간법)
  • Optimal(shortest) path between $q_1$ and $q_2$

4. Line and Circle

• Interpolate position linearly

• Circle detail
  • point must be non collinear(동일선상)
  • N = $v_1$ x $v_2$
• direction N stays the same, only magnitude changed
• normalize N after the product

5. spline(매끄러운 곡선)

• The operator needs a “smooth” path between points

5.1 Practice

• place control point along targets

6 transition(변화)

• round edge
• sharp edges are a problem
  • smooth geometrical path
  • increase path speed
  • reduces mechanical wear

7 path length and corrections

• analytical calculation for lines and circles

• numerically calculation for PTP and splines

• external path corrections

• happen at runtime, not planned, not predictable
• typical case : conveyor tracking(increased productivity)
• position limits must be monitored at runtime
• path length changes, so dynamic limits must also be monitored at runtime