Sample-based motion planning in high-dimensional and differentially-constrained systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 115-124).State of the art sample-based path planning algorithms, such as the Rapidly-exploring Random Tree (RRT), have proven to be effective in path planning for systems subject to complex kinematic and geometric constraints. The performance of these algorithms, however, degrade as the dimension of the system increases. Furthermore, sample-based planners rely on distance metrics which do not work well when the system has differential constraints. Such constraints are particularly challenging in systems with non-holonomic and underactuated dynamics. This thesis develops two intelligent sampling strategies to help guide the search process. To reduce sensitivity to dimension, sampling can be done in a low-dimensional task space rather than in the high-dimensional state space. Altering the sampling strategy in this way creates a Voronoi Bias in task space, which helps to guide the search, while the RRT continues to verify trajectory feasibility in the full state space. Fast path planning is demonstrated using this approach on a 1500-link manipulator. To enable task-space biasing for underactuated systems, a hierarchical task space controller is developed by utilizing partial feedback linearization. Another sampling strategy is also presented, where the local reachability of the tree is approximated, and used to bias the search, for systems subject to differential constraints. Reachability guidance is shown to improve search performance of the RRT by an order of magnitude when planning on a pendulum and non-holonomic car. The ideas of task-space biasing and reachability guidance are then combined for demonstration of a motion planning algorithm implemented on LittleDog, a quadruped robot. The motion planning algorithm successfully planned bounding trajectories over extremely rough terrain.by Alexander C. Shkolnik.Ph.D

Exponentially Stabilizing Controllers for Multi-Contact 3D Bipedal Locomotion

Models of bipedal walking are hybrid with continuous-time phases representing the Lagrangian stance dynamics and discrete-time transitions representing the impact of the swing leg with the walking surface. The design of continuous-time feedback controllers that exponentially stabilize periodic gaits for hybrid models of underactuated 3D bipedal walking is a significant challenge. We recently introduced a method based on an iterative sequence of optimization problems involving bilinear matrix inequalities (BMIs) to systematically design stabilizing continuous-time controllers for single domain hybrid models of underactuated bipedal robots with point feet. This paper addresses the exponential stabilization problem for multi-contact walking gaits with nontrivial feet. A family of parameterized continuous-time controllers is proposed for different phases of the walking cycle. The BMI algorithm is extended to the multi-domain hybrid models of anthropomorphic 3D walking locomotion to look for stabilizing controller parameters. The Poincaré map is addressed and a new set of sufficient conditions is presented that guarantees the convergence of the BMI algorithm to a stabilizing set of controller parameters at a finite number of iterations. The power of the algorithm is ultimately demonstrated through the design of stabilizing virtual constraint controllers for dynamic walking of a 3D humanoid model with 28 state variables and 275 controller parameters

Exponentially Stabilizing Controllers for Multi-Contact 3D Bipedal Locomotion

Models of bipedal walking are hybrid with continuous-time phases representing the Lagrangian stance dynamics and discrete-time transitions representing the impact of the swing leg with the walking surface. The design of continuous-time feedback controllers that exponentially stabilize periodic gaits for hybrid models of underactuated 3D bipedal walking is a significant challenge. We recently introduced a method based on an iterative sequence of optimization problems involving bilinear matrix inequalities (BMIs) to systematically design stabilizing continuous-time controllers for single domain hybrid models of underactuated bipedal robots with point feet. This paper addresses the exponential stabilization problem for multi-contact walking gaits with nontrivial feet. A family of parameterized continuous-time controllers is proposed for different phases of the walking cycle. The BMI algorithm is extended to the multi-domain hybrid models of anthropomorphic 3D walking locomotion to look for stabilizing controller parameters. The Poincaré map is addressed and a new set of sufficient conditions is presented that guarantees the convergence of the BMI algorithm to a stabilizing set of controller parameters at a finite number of iterations. The power of the algorithm is ultimately demonstrated through the design of stabilizing virtual constraint controllers for dynamic walking of a 3D humanoid model with 28 state variables and 275 controller parameters

Stabilizing Highly Dynamic Locomotion in Planar Bipedal Robots with Dimension Reducing Control.

In the field of robotic locomotion, the method of hybrid zero dynamics (HZD) proposed by Westervelt, Grizzle, and Koditschek provided a new solution to the canonical problem of stabilizing walking in planar bipeds. Original walking experiments on the French biped RABBIT were very successful, with gaits that were robust to external disturbances and to parameter mismatch. Initial running experiments on RABBIT were cut short before a stable gait could be achieved, but helped to identify performance limiting aspects of both the physical hardware of RABBIT and the method of hybrid zero dynamics. To improve upon RABBIT, a new robot called MABEL was designed and constructed in collaboration between the University of Michigan and Carnegie Mellon University. In light of experiments on RABBIT and in preparation for experiments on MABEL, this thesis provides a theoretical foundation that extends the method of hybrid zero dynamics to address walking in a class of robots with series compliance. Extensive new design tools address two main performance limiting aspects of previous HZD controllers: the dependence on non-Lipschitz finite time convergence and the lack of a constructive procedure for achieving impact invariance when outputs have relative degree greater than two. An analytically rigorous set of solutions - an arbitrarily smooth stabilizing controller and a constructive parameter update scheme - is derived using the method of Poincare sections. Additional contributions of this thesis include the development of sample-based virtual constraints, analysis of walking on a slope, and identification of dynamic singularities that can arise from poorly chosen virtual constraints.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58477/1/morrisbj_1.pd

Design of high-performance legged robots: A case study on a hopping and balancing robot

The availability and capabilities of present-day technology suggest that legged robots should be able to physically outperform their biological counterparts. This thesis revolves around the philosophy that the observed opposite is caused by over-complexity in legged robot design, which is believed to substantially suppress design for high-performance. In this dissertation a design philosophy is elaborated with a focus on simple but high performance design. This philosophy is governed by various key points, including holistic design, technology-inspired design, machine and behaviour co-design and design at the performance envelope. This design philosophy also focuses on improving progress in robot design, which is inevitably complicated by the aspire for high performance. It includes an approach of iterative design by trial-and-error, which is believed to accelerate robot design through experience. This thesis mainly focuses on the case study of Skippy, a fully autonomous monopedal balancing and hopping robot. Skippy is maximally simple in having only two actuators, which is the minimum number of actuators required to control a robot in 3D. Despite its simplicity, it is challenged with a versatile set of high-performance activities, ranging from balancing to reaching record jump heights, to surviving crashes from several meters and getting up unaided after a crash, while being built from off-the-shelf technology. This thesis has contributed to the detailed mechanical design of Skippy and its optimisations that abide the design philosophy, and has resulted in a robust and realistic design that is able to reach a record jump height of 3.8m. Skippy is also an example of iterative design through trial-and-error, which has lead to the successful design and creation of the balancing-only precursor Tippy. High-performance balancing has been successfully demonstrated on Tippy, using a recently developed balancing algorithm that combines the objective of tracking a desired position command with balancing, as required for preparing hopping motions. This thesis has furthermore contributed to several ideas and theories on Skippy's road of completion, which are also useful for designing other high-performance robots. These contributions include (1) the introduction of an actuator design criterion to maximize the physical balance recovery of a simple balancing machine, (2) a generalization of the centre of percussion for placement of components that are sensitive to shock and (3) algebraic modelling of a non-linear high-gravimetric energy density compression spring with a regressive stress-strain profile. The activities performed and the results achieved have been proven to be valuable, however they have also delayed the actual creation of Skippy itself. A possible explanation for this happening is that Skippy's requirements and objectives were too ambitious, for which many complications were encountered in the decision-making progress of the iterative design strategy, involving trade-offs between exercising trial-and-error, elaborate simulation studies and the development of above-mentioned new theories. Nevertheless, from (1) the resulting realistic design of Skippy, (2) the successful creation and demonstrations of Tippy and (3) the contributed theories for high-performance robot design, it can be concluded that the adopted design philosophy has been generally successful. Through the case study design project of the hopping and balancing robot Skippy, it is shown that proper design for high physical performance (1) can indeed lead to a robot design that is capable of physically outperforming humans and animals and (2) is already very challenging for a robot that is intended to be very simple

Hopping, Landing, and Balancing with Springs

This work investigates the interaction of a planar double pendulum robot and springs, where the lower body (the leg) has been modified to include a spring-loaded passive prismatic joint. The thesis explores the mechanical advantage of adding a spring to the robot in hopping, landing, and balancing activities by formulating the motion problem as a boundary value problem; and also provides a control strategy for such scenarios. It also analyses the robustness of the developed controller to uncertain spring parameters, and an observer solution is provided to estimate these parameters while the robot is performing a tracking task. Finally, it shows a study of how well IMUs perform in bouncing conditions, which is critical for the proper operation of a hopping robot or a running-legged one

Bio-Inspired Robotics

Modern robotic technologies have enabled robots to operate in a variety of unstructured and dynamically-changing environments, in addition to traditional structured environments. Robots have, thus, become an important element in our everyday lives. One key approach to develop such intelligent and autonomous robots is to draw inspiration from biological systems. Biological structure, mechanisms, and underlying principles have the potential to provide new ideas to support the improvement of conventional robotic designs and control. Such biological principles usually originate from animal or even plant models, for robots, which can sense, think, walk, swim, crawl, jump or even fly. Thus, it is believed that these bio-inspired methods are becoming increasingly important in the face of complex applications. Bio-inspired robotics is leading to the study of innovative structures and computing with sensory–motor coordination and learning to achieve intelligence, flexibility, stability, and adaptation for emergent robotic applications, such as manipulation, learning, and control. This Special Issue invites original papers of innovative ideas and concepts, new discoveries and improvements, and novel applications and business models relevant to the selected topics of ``Bio-Inspired Robotics''. Bio-Inspired Robotics is a broad topic and an ongoing expanding field. This Special Issue collates 30 papers that address some of the important challenges and opportunities in this broad and expanding field

Embedding the Generalized Acrobot into the N-Link with an Unactuated Cyclic Variable and Its Application to Walking Design

International audienceThe Acrobot is the well-known and widely studied underactuated mechanical system having two links and one actuated joint between them. It may be also viewed as the simplest possible walking like mechanism without knees and the ankle-joint actuation, alternatively also referred to as the underactuated Compass gait walker. To extend techniques used to control the Acrobot to a more general underactuated n-link having an unactuated cyclic variable, this paper defines the so-called generalized Acrobot. Further, it is shown that for every set of virtual constraints there exists a generalized Acrobot that is linearly embedded into this n-link. Based on this property and results valid for the Acrobot, walking strategies for the n-link are provided. Important achievement here is that the exponentially stable tracking during the swing phase only is possible, i.e. the stabilizing effect of the impact map is not needed. Computer simulations of the 4-link case are provided

Modular Hopping and Running via Parallel Composition

Though multi-functional robot hardware has been created, the complexity in its functionality has been constrained by a lack of algorithms that appropriately manage flexible and autonomous reconfiguration of interconnections to physical and behavioral components. Raibert pioneered a paradigm for the synthesis of planar hopping using a composition of ``parts\u27\u27: controlled vertical hopping, controlled forward speed, and controlled body attitude. Such reduced degree-of-freedom compositions also seem to appear in running animals across several orders of magnitude of scale. Dynamical systems theory can offer a formal representation of such reductions in terms of ``anchored templates,\u27\u27 respecting which Raibert\u27s empirical synthesis (and the animals\u27 empirical performance) can be posed as a parallel composition. However, the orthodox notion (attracting invariant submanifold with restriction dynamics conjugate to a template system) has only been formally synthesized in a few isolated instances in engineering (juggling, brachiating, hexapedal running robots, etc.) and formally observed in biology only in similarly limited contexts. In order to bring Raibert\u27s 1980\u27s work into the 21st century and out of the laboratory, we design a new family of one-, two-, and four-legged robots with high power density, transparency, and control bandwidth. On these platforms, we demonstrate a growing collection of $\{$body, behavior$\}$ pairs that successfully embody dynamical running / hopping ``gaits\u27\u27 specified using compositions of a few templates, with few parameters and a great deal of empirical robustness. We aim for and report substantial advances toward a formal notion of parallel composition---embodied behaviors that are correct by design even in the presence of nefarious coupling and perturbation---using a new analytical tool (hybrid dynamical averaging). With ideas of verifiable behavioral modularity and a firm understanding of the hardware tools required to implement them, we are closer to identifying the components required to flexibly program the exchange of work between machines and their environment. Knowing how to combine and sequence stable basins to solve arbitrarily complex tasks will result in improved foundations for robotics as it goes from ad-hoc practice to science (with predictive theories) in the next few decades