Elie A. Shammas

Geometric Motion Planning Analysis for Two Classes of Underactuated Mechanical Systems

In this paper we generate gaits for two types of underactuated mechanical systems: principally kinematic and purely mechanical systems. Our goal is to specify inputs in the form of gaits, that is, a sequence of controlled shape changes of a multi-bodied mechanical system that when executed would produce a desired change in the unactuated position or orientation variables of the entire mechanical system. In other words, we want to indirectly control the unactuated degrees of freedom of the mechanical system utilizing a controlled “internal” shape change. More precisely, in this paper we develop a gait evaluation tool which easily measures the change of position, computed in a body-attached coordinate frame, due to any closed curve in the shape space. This evaluation tool is simple enough that we can use it to generate gaits or to design curves that move the mechanical system along a desired direction. Finally, we verify that this gait analysis technique applies to two seemingly different classes of mechanical systems, purely mechanical and principally kinematic systems, and unify the gait generation problem for both classes.

New joint design for three-dimensional hyper redundant robots

This paper presents a novel compact design for a two degrees of freedom (DOF) joint mechanism. The joint is optimized for compactness, strength and range of motion which makes it ideal for constructing spatial or three-dimensional hyper redundant robots. We also identify and classify various prior joint designs that led to the development of this new concept. Finally, we present the joint forward kinematics, and force and torque calculations to verify the joints range of motion and mechanical advantage.

Toroidal skin drive for snake robot locomotion

Small robots have the potential to access confined spaces where humans cannot go. However, the mobility of wheeled and tracked systems is severely limited in cluttered environments. Snake robots using biologically inspired gaits for locomotion can provide better access in many situations, but are slow and can easily snag. This paper introduces an alternative approach to snake robot locomotion, in which the entire surface of the robot provides continuous propulsive force to significantly improve speed and mobility in many environments.

Towards a Unified Approach to Motion Planning for Dynamic Underactuated Mechanical Systems with Non-holonomic Constraints

In this paper, we generalize our prior results in motion analysis to design gaits for a more general family of underactuated mechanical systems. In particular, we analyze and generate gaits for mixed mechanical systems which are systems whose motion is simultaneously governed by both a set of non-holonomic velocity constraints and a notion of a generalized momentum being instantaneously conserved along allowable directions of motion. Through proper recourse to geometric mechanics, we are able to show that the resulting motion from a gait has two portions: a geometric and a dynamic contribution. The main challenge in motion planning for a mixed system is understanding how to separate the geometric and dynamic contributions of motion due to a general gait, thus simplifying gait analysis. In this paper, we take the first step towards addressing this challenge in a generalized framework. Finally, we verify the generality of our approach by applying our techniques to novel mechanical systems which we introduce in this paper as well as by verifying that seemingly different prior motion planning results could actually be explained using the gait analysis presented in this paper.

Natural Gait Generation Techniques for Multi-bodied Isolated Mechanical Systems

This paper investigates how to generate cyclic gaits for multi-bodied isolated mechanical systems whose configuration space is represented by a trivial fiber bundle. We describe how to generate gaits in the base space of the fiber bundle, or the shape space of the robot on which we assume full control. Such gaits are guaranteed to generate a non-zero motion along the fiber space, i.e., a net change in the position of the robot, while making sure that the robot’s shape is unchanged after a complete cycle. The gait generation technique presented in this paper is intuitive; it involves dividing the base space into well defined regions and devising a set of simple rules on how to generate curves in such regions. Not only do such curves guarantee non-zero position change but also do allow for gait optimization.

Natural Gait Generation Techniques for Principally Kinematic Mechanical Systems

In this paper we present a novel gait analysis technique which can directly be used to synthesize gaits for a broad class of mechanical systems. We build upon prior work in locomotion mechanics, however we take a different approach to generate gaits that yield absolute motion of the mechanical system. We present a systematic analysis to control all parameters of a proposed type of gait which eliminates the need for intuition and guesswork as was required in the prior work. The main contribution of the paper is relating position change or motion in the ber space to a volume integral bounded by closed curves on a two dimensional manifold embedded in the base space or shape space of the robot. Not only does our method remove the restriction of using sinusoidal gaits as was the case in the prior work but it also allows for generating optimal gaits by solving a variational problem rather than solving a dynamic programming problem as was the case in the prior work.

Towards automated gait generation for dynamic systems with non-holonomic constraints

In this paper we generate gaits for dynamics systems that are subject to non-holonomic velocity constraints. These systems are referred to as mixed non-holonomic systems. The motion of such systems is governed by both the non-holonomic constraints acting on the system and a system of differential equations constraining the evolution of generalized momentum. We propose a method that utilizes both governing motions, that is, satisfying all the constraints and instantaneously conserving momentum along un-restricted directions, to generate gaits for systems like the snakeboard, which belongs to the family of mixed non-holonomic systems. We accomplish this by defining a new scaled momentum variable. This scaled momentum allows us to easily explore the design of gaits that causes momentum to evolve such that a desired non-trivial motion results

Ground segmentation and occupancy grid generation using probability fields

This paper proposes a novel technique for segmenting the ground plane and at the same time estimating the occupancy probability of each point in a scene. Using a stereo camera rig, our system first calculates a disparity map and transforms it to a v-disparity map, which is then filtered and processed to generate a corresponding probability field. The probability field generated is then used for precise segmentation of ground planes as well as for the generation of occupancy grids. Unlike what is proposed in the prior art, our system requires minimal initialization and is independent of the stereo sensor characteristics as well as the parameters of the disparity algorithm. More importantly, our technique does not require any prior assumption about the terrain visual characteristics. Experimental results using sequences of images from two different data sets are presented to validate the proposed methods.

Motion planning for the Snakeboard

This paper provides an analytical solution to the motion-planning problem for the Snakeboard. Given a desired planar trajectory in the fiber space, an explicit solution is computed for the controllable inputs in the base space that locomote the Snakeboard along a given trajectory. The motion-planning problem or gait generation problem is solved for the generalized Snakeboard where the orientation of the wheels is not coupled, as well as for several special configurations of the Snakeboard.

An Analytic Motion Planning Solution for the Snakeboard

This paper provides a closed-form analytical solution to the motion planning problem for the Snakeboard. Given a desired planar trajectory in the fiber space, an explicit solution is computed for the gaits in the base space that locomote the Snakeboard along the desired trajectory. This is achieved by introducing a new momentum-like variable that simplifies the Snakeboard’s equations of motion to allow for such an explicit gait generation technique.