Multi-surface contact interactions in articulated rigid-body systems : physical modeling, experimental validation and efficient simulation
Keywords: Mechanical Engineering.

Advanced robotic manipulation holds the key to extending human reach to new frontiers, and improving the quality of human life. Modern techniques of programming robotic manipulation strategies leverage force feedback, task-oriented control and expert task demonstration through visual-haptic interfaces. Developing robust manipulation strategies requires accurate and efficient models for simultaneous contacts between robots and other parts of their workspace. Such contact models are commonly embedded into compliant manipulation strategies, and into the simulation tools used to design them. One of the key challenges in modeling simultaneous multi-contact interactions between articulated bodies lies in compactly describing the dynamics of the system with the contact constraints. The classical approach of resolving multi-contact interactions for articulated bodies is to solve a collection of unilateral contact constraints and bilateral joint constraints on free rigid bodies. However, this approach is computationally inefficient, and produces inaccurate robot motion, that needs ad-hoc post-correction. Moreover, smooth body geometry is typically discretized into polygon soups, resulting in a redundant description of contact constraints, particularly when contact occurs across a line, curve, or a surface patch, such as a coffee mug placed flat against a table. Discretizing the smooth geometric surfaces of contact into a set of contact points not only results in nonphysical jittery motion and poor simulator performance, but also results in an incorrect estimate of the contact force exerted by the robot on its environment, an essential sensory estimate for simulation of compliant manipulation strategies. There are two main goals that I set out to achieve in this work: (i) improve the computational speed of multi-contact resolution for articulated body systems without compromising physical correctness, and (ii) develop a theoretical understanding of the contact-constrained dynamics of such systems, that generalizes to non-polyhedral body geometry. To regulate the complexity of achieving the above goals, an overarching assumption in this work is that the system is composed of rigid articulated bodies, where rigidity is defined to imply that neither deformation nor interpenetration is admissible between the bodies in contact. The first contribution of this thesis towards the above goals is to develop and experimentally validate a new approach for multi-contact modeling in robotic systems. This Contact Space Resolution Model (CSR model) model addresses the problem of simultaneously enforcing multiple joint and contact constraints in articulated rigid body (ARB) systems. Building on the theory of operational space manipulator dynamics and control, it is shown that through the proper choice of a set of contact-space coordinates, the instantaneous dynamics of the ARB system can be partitioned into two dynamically-consistent complementary sub-spaces - the contact space and the null space. The projected dynamics in the contact space is governed by the effective mass and effective rotational inertia of the two bodies at the contact points, whereas the projected dynamics in the null-space is undisturbed by the contact forces. This latter property is a generalization of the principle of momentum conservation to ARB systems. A series of single- and two-point collision experiments conducted on free-hanging multi-link pendulums demonstrate that the CSR Model accurately predicts the post-collision system state. Moreover, for the first time, it is shown experimentally that the projection of system dynamics into the mutually complementary contact space and null space is a physically verifiable phenomenon. To address the problem of constraint over-redundancy introduced by the assumption that contact occurs across a finite set of points, a new Shared Contact Frame (SC-Frame) theory is developed. The SC-Frame theory extends the CSR model by a choice of contact-space coordinates that corresponds to the infinitesimal relative motion between two links in contact at a chosen frame. For a particular choice of frame, the possible obstructive contact forces (or wrenches in general) lie within a convex cone, which is normal to the contact-space acceleration. Frictional force and moment act in a symmetric, convex subset of the wrench space, as per Coulomb's dry friction model. An efficient SC-Frame Planar-Contact algorithm is developed for the particular case where the contact configuration between any two links is a set of co-planar contact patches. In this algorithm, the location of the SC-Frame is resolved simultaneously with the contact wrench, under the assumption that the frame lies at the center of pressure of the contact pressure distribution. As a result, the geometric location of the resolved frame origin is physically significant, and naturally captures impending transitions in the contact state between the bodies. Simulation results are presented with bodies modeled geometrically as unions of convex primitives. It is demonstrated that the method results in smooth motion, qualitatively correct contact state transitions, reliable contact force estimates and a significant improvement in computational speed over conventional multi-point contact solvers. Through the course of this research endeavour, I also worked on several other applied robotics projects ranging from the development of the underwater humanoid robot, Ocean One, to the conceptual prototyping of an underground drilling robot for gold mining. Due to their tangential nature to the subject at hand, these projects are not discussed in this thesis, but may be found in additional publications