• Control
• Grasping
• Manipulation
• Motion Planning
• Planning
• Robotics

There are many reasons why a compliant robot is expected to perform better than a rigid one in interaction tasks, which include limitation of interaction forces, resilience to modeling errors, robustness, naturalness of motion, and energy efficiency. Most of these reasons are apparent if one thinks of how the human body interacts with its environment.
However, most of the work in robotic planning and control of interaction has been traditionally developed for rigid robot models. Indeed, planning and control for compliant robots can be substantially harder.

In this thesis, I propose the point of view that the difficulties encountered in planning and control for soft robots are at least in part due to the fact that the same approaches previously used for rigid robots are used as a starting point and adapted. On the opposite, if new methods are considered that start from consideration of compliance from the very beginning, the planning and control problems can be of comparable difficulty, or even substantially simpler, than their rigid counterpart. I will argue this thesis with two main examples.

The first part of this thesis presents a new approach to integrate motion planning and control for robots in interaction. One of the peculiarities of interaction tasks is that the robot limbs and the environment form "closed kinematic chains". If rigid models are considered, the dynamics of robots in interaction become constrained, and Differential Algebraic Equations replace Ordinary Differential Equations, i.e. typically a much harder problem to deal with. However, in the thesis I show that this is not necessarily so. Indeed, consideration of compliance allows to have a more tractable mathematical model of interacting systems, and to introduce more sophisticated control approaches. Specifically, we present a novel geometric control scheme under which for constrained robot systems we achieve decoupled interaction control (i.e. make position errors irrelevant to force control, and viceversa).

Based on this result, it is possible to decouple the planning problem in two separate aspects. On one side, we make dealing with motion planning of the constrained system easier by relaxing the geometric constraint, i.e. replacing the lower--dimensional constraint manifold with a narrow but full-dimensional boundary layer. This allows us to plan motion using state-of-the-art methods, such as RRT*, on points within the boundary layer, which we can efficiently sample.
On the other side we control interaction forces, i.e. forces generated by displacements in the perpendicular direction to the tangent space of the constraint manifold. Thanks to the (locally) noninteracting control characteristic of our scheme, the two controllers can be applied separately and in sequence, so that the interaction force controller can correct for any discrepancies resulting from the boundary layer approximation used in the constrained position controller.

The geometric noninteracting controller can be applied both in simulation for planning, and in real time for execution control. Moreover, while it does rely on considering a model of compliance in the system, it does not make any assumption on the amount of compliance in the system - or in other words, it applies equally well to stiff but elastic robots. The final outcome of the two-stage planner is an effective (possibly optimal from RRT*) trajectory that satisfies constraint with arbitrarily good approximation, asymptotically rejecting perturbations coming from sampled displacements.

The second part of this thesis is dedicated to study grasp planning for hands that are simple -- in the sense of low number of actuated degrees of freedom -- but soft, i.e. continuously deformable in an infinity of possible shapes through interaction with objects. Once again, the use of such "soft hands" brings about a change of paradigm in grasp planning with respect to classical rigid multi-dof grasp planning, which only apparently makes the problem harder. However, in this thesis I show that thanks to the correct combination of compliance and underactuation of soft hands, together with the set of all possible physical interactions between the hand, the object and the environment, the grasping problem can be redefined. The new definition includes the possible combination of hand-object functional interactions which I address as "Enabling Constraints". The use of Enabling Constraints constitutes a rather new challenge for existing grasping algorithms: adaptation to totally or partially unknown scenes remains a difficult task, toward which only some approaches have been investigated so far. In this thesis I present a first approach to the study of this novel kind of manipulation. It is based on an accurate simulation tool and starts from the considerations that hand compliance can be used to adapt to the shape of the surrounding objects and that rather than considering the environment as and obstacle to avoid, it can be used in turn to functionally shape the hand. I show that thanks to this functionality the problem of generating grasping postures for soft hands can be reduced to grasp basic geometries (e.g. cylinders or boxes) in which the geometry of the object can be decomposed.