In this thesis, I present novel strategies for controlling objects with high degrees of freedom for the purpose of robotic control and computer animation, including articulated objects such as human bodies or robots and deformable objects such as ropes and cloth. Such control is required for common daily movements such as folding arms, tying ropes, wrapping objects and putting on clothes. Although there is demand in computer graphics and animation for generating such scenes, little work has targeted these problems. The difficulty of solving such problems are due to the following two factors: (1) The complexity of the planning algorithms: The computational costs of the methods that are currently available increase exponentially with respect to the degrees of freedom of the objects and therefore they cannot be applied for full human body structures, ropes and clothes . (2) Lack of abstract descriptors for complex tasks. Models for quantitatively describing the progress of tasks such as wrapping and knotting are absent for animation generation. In this work, we employ the concept of a task-centric manifold to quantitatively describe complex tasks, and incorporate a bi-mapping scheme to bridge this manifold and the configuration space of the controlled objects, called an object-centric manifold. The control problem is solved by first projecting the controlled object onto the task-centric manifold, then getting the next ideal state of the scenario by local planning, and finally projecting the state back to the object-centric manifold to get the desirable state of the controlled object. Using this scheme, complex movements that previously required global path planning can be synthesised by local path planning. Under this framework, we show the applications in various fields. An interpolation algorithm for arbitrary postures of human character is first proposed. Second, a control scheme is suggested in generating Furoshiki wraps with different styles. Finally, new models and planning methods are given for quantitatively control for wrapping/ unwrapping and dressing/undressing problems.