A global approach to kinematic path planning to robots with holonomic and nonholonomic constraints
Robots in applications may be subject to holonomic or nonholonomic constraints. Examples of holonomic constraints include a manipulator constrained through the contact with the environment, e.g., inserting a part, turning a crank, etc., and multiple manipulators constrained through a common payload. Examples of nonholonomic constraints include no-slip constraints on mobile robot wheels, local normal rotation constraints for soft finger and rolling contacts in grasping, and conservation of angular momentum of in-orbit space robots. The above examples all involve equality constraints; in applications, there are usually additional inequality constraints such as robot joint limits, self collision and environment collision avoidance constraints, steering angle constraints in mobile robots, etc. The problem of finding a kinematically feasible path that satisfies a given set of holonomic and nonholonomic constraints, of both equality and inequality types is addressed. The path planning problem is first posed as a finite time nonlinear control problem. This problem is subsequently transformed to a static root finding problem in an augmented space which can then be iteratively solved. The algorithm has shown promising results in planning feasible paths for redundant arms satisfying Cartesian path following and goal endpoint specifications, and mobile vehicles with multiple trailers. In contrast to local approaches, this algorithm is less prone to problems such as singularities and local minima.