PhD Thesis

Motion Planning under Differential Constraints

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  • Started: 01/07/2016


The goal of this thesis is to provide reliable algorithms for solving the kinodynamic motion planning problem on constrained robotic systems. Given a kinematic and dynamic model of the system, and a geometric model of the environment, this problem consists in computing the required force inputs needed to move a robot between two prescribed states, while respecting the following constraints:

(1) Kinematic constraints which are those only involving position and velocity coordinates of the mechanism. These include constraints due to sliding and rolling contacts between bodies, closed kinematic loops inherent to the robot structure or to the task to be executed, collision avoidance, and joint limits.

(2) Dynamic constraints which are those involving position, velocity and acceleration coor- dinates, and the forces acting on the system. These correspond to the equations of motion of the robot, limits on the actuator or constraint forces, or existing velocity and acceleration bounds.

Although many solutions to the kinodynamic planning problem have been proposed, to the best of our knowledge, no satisfactory approach has been given for constrained systems whose state space is not globally parametrizable. Therefore, the kinodynamic planning problem remains open for the class of systems herein considered.