Background Information on Robot Motion Planning


Naomi Fox
Information taken from Computational Geometry, M. de Berg


Dictionary of Terms


  • articulated robot - a robot arm, which consists of links, connected by joints
  • base - one end of arm which is firmly connected to ground
  • hand - other end of arm, not fixed
  • revolute joint - allows the links to rotate around the joint, like an elbow
  • prismatic joint - allows one of the links to slide in and out
  • car-like robot - cannot move sideways, have certain minimum turning radius
  • work-space - restricted environment of robot
  • Configuration space - the parameter space of a robot R denoted by C(R). A point p in this configuration space corresponds to a certain placement R(p) of the robot in the work space. The configuration space of a translating robot in the plane is the 2-dimensional Euclidan plane.


    Example of a 3D articulated robot taken from Dan Challou's and Maria Gini's Articulated Robot Research page

    Simplification of Problem


    To have the work space equal to the world makes an extremely complex problem. In Robot Motion Planning, it is important to place constraints on a problem in order to get a smaller task that is possible to solve.

    An often used simplification of robot motion planning problem requires:
  • Environment is a planar region with polygonal obstacles.
  • The robot itself is polygonal.
  • Environment is static and known to the robot.

    With this simplification it is much easier to apply elements of computational geometry to the problem.

    Example of a Workspace with this simplification in a robot motion planning problem


    Work Space and Configuration Space



    Let R be a simple polygon robot moving around in a 2-d environment, or work space, consisting of a set S = {P1,.., Pt} obstacles. A placement, or configuation, of the robot can be specified by a translation vector.
    Another way of viewing this is in terms of a reference point. We can specify a placement of R by stating the coordinates of the reference point if the robot is in the given placement, so R(x,y) specifies that the robot is placed with its refernce point at (x,y).

    If the robot can change its orientation by rotation, we need an extra parameter, angle, to specify the orientation of a robot, so then R(x,y,angle) denotes the robot at its reference point (x,y) and rotated through an agle.

    The degrees of freedom (DOF) of a robot is another parameter.
  • two - planar robots that can only translate
  • three - planar robots that can rotate and translate
    The number of parameters needed for a robot in 3-dimensional space is higher: a translating robot in R^3 has three degrees of freedom, and a robot that is free to translate and roateate in R^3 has six degres of freedom.

    Configuration space - the parameter space of a robot R denoted by C(R). A point p in this configuration space corresponds to a certain placement R(p) of the robot in the work space. The configuration space of a translating robot in the plane is the 2-dimensional Euclidan plane.

    The difference between the work space and the configuration space:
    The work space is where the robot actually moves around = the real world

    The configuration space is the parameter space of the robot.

    Forbidden configuration space - Cforb(R,S) - points corresponding to placements where the robot intersects one of the obstacles in S which are forbidden.

    Configuration-space obstacle (C-obstacle) - the resultant set when an obstacle P is mapped to the set of points p in configuration space such that R(p) intersects P

    We choose the opiton that obstacles are open sets, which means tha the robot is allowed to touch them. (If they were closed, the robot would not be allowed to do so.)



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