Trajectory planning for underactuated kinodynamic systems

This thesis describes trajectory planning algorithms for a class of second-order underactuated mechanical systems called kinematically controllable systems. For kinematically controllable systems, the problem of planning fast collision-free trajectories can be decoupled into the computationally simpler problems of path planning for a kinematic system in C-space followed by time-optimal time scaling of the kinematic paths. Path planners using variations of randomized algorithms like Rapidly-Exploring Random Trees (RRT) and Visibility-based Probabilistic Roadmaps (Vis-PRM) are described for efficient computation of fast trajectories. The inverse kinematics of the robots are exploited for accurate path planning such that the robot can exactly reach its goal state. The resulting kinematic paths computed from the path planners are time-scaled to produce fast output trajectories. Extensive numerical simulations have been done to test the performance of the path planners.