Summary of the Invited Talks

Balancing Made Simple

By: Roy Featherstone

This talk describes some basic principles that can be used to simplify the problem of balancing, and to achieve high-performance balancing in the sense that the robot can make large, fast movements without losing its balance. These principles are: (1) treat balancing as a physical process instead of a control theory exercise; (2) express the balancing behaviour in a simple form; (3) seek to control the balancing behaviour only; and (4) lean in anticipation of future commanded motions.

Model Predictive Control for Cheetah 3

By: Sangbae Kim

The talk will discuss the control algorithm of the MIT Cheetah 3 in conjunction with the hardware design. The robot is designed to minimize distal inertia/masses to improve the dynamic capability and efficiency of locomotion. This design architecture not only allows for better force control bandwidth upon contacts followed by impacts but also allows us to focus on body dynamics rather than dealing with a full complex model. Utilizing the design characteristics, our MPC (model predictive control) use a simple model of body to determine ground reaction force trajectories of each steps. Using this approach, the MIT cheetah can run at 3m/s and walk on a very rough terrains including stairs without relying on vision.

Spatially Quantized Dynamics, a new approach for model discretization

By: Shuuji Kajita

To treat continuous robot dynamic models, we usually discretizes it with a unit time step. Discretizing it with a unit spatial step, we obtain Spatially Quantized Dynamics (SQD) which yields simple but nonlinear equation. It is shown that we can easily solve the ZMP based walking pattern generation by using a spatially discretized linear inverted pendulum along the walking direction. By using this framework, we have realized a walking control with stretched-knees and wide strides.

Design and control of locomotor systems based on locomotor sub-functions and sensor-motor-maps

By: Andre Seyfarth

Human locomotion is a complex movement task, which can be divided into a set of locomotor subfunctions. These subfunction comprise stance leg function, swing leg function and balance. Each of these locomotor subfunctions requires a specific control of individual muscles in the human body. We propose a novel method based on sensor-motor-maps to identify the appropriate motor control settings based on sensory feedback loops. Based on template models, both the biomechanical as well as the neuromuscular dynamics of gait can be studies and described at different levels of detail.

Accurate Modeling, Control and Embedding of Templates for Planar Running

By: Uluc Saranli

Spring-mass models with various features and extensions have been widely used as dynamical templates for running and walking but their accurate and efficient embedding in pyhsical platforms has been challenging. In this talk will first present a brief overview of our work in finding accurate analytic solutions to the dynamics of planar spring-mass models, together with their applications in template-based control of locomotion. I will then present the idea of using virtually tunable damping as a control strategy on these templates, allowing more efficient exploitation of their natural dynamics. Finally, I will present more recent results on the embedding of these templates and the tunable damping strategy on increasingly complex physical platforms.

Template Composition for Synthesis of New Behaviors from Simpler Constituents

By: Avik De (Daniel E Koditschek)

Raibert pioneered a paradigm for the synthesis of planar hopping using a composition of “parts”: 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. Framed in the context of understanding and extending that work, we provide an update on our research progress on 3 fronts: (a) we have demonstrated dynamical running/hopping “gaits” on a variety of platforms (including a quadruped and a tailed biped) using compositions of decoupled controllers, with few parameters and a great deal of empirical robustness; (b) we have formulated the problem of designing robots to facilitate the success of such compositional controllers; and (c) we have developed mathematical tools to model the systems that can be controlled in this way as well as provide guarantees of their stability at design-time. Lastly, we also describe the utility of an analytical understanding of these reduced-order models for template-based online planning.

To embed biped motion skill into inverted pendulum model

By: Tomomichi Sugihara

The analogy of a biped robot to an inverted pendulum is naturally derived based on the dynamics. It helps an intuitive understanding of the system and leads to an idea to control the center of mass (COM) by manipulating the zero-moment point (ZMP). On the other hand, it loses an explicit representation of switch of support, which is another characteristic of the biped motion. In this talk, a controller that embeds a motion skill not only to stabilize COM but also to initiate an appropriate switch of support into the inverted pendulum is presented.

Dynamic locomotion in horizontal and vertical domains: templates, scaling, and adaptations for multi-modal behaviors

By: Jonathan E Clark

Planar reduced order dynamic models of running and walking behaviors capture different aspects of the fundamental motions, depending on the behavior and the 2D plane chosen for the abstraction. In this talk I will summarize some of the similarities and the differences between models such as SLIP and LLS for horizontal plane motion with those utilized in the pendular (Full-Goldman) model of vertical running.

Despite their differences, the fact that animals such as cockroaches and geckos have been shown to be able to exhibit the motions characteristic of each of these models suggests that robotic platforms should be able to move in similar multi-modal, dynamic manners. I will review some early and some ongoing work to build devices that can anchor these temples for both level ground and vertical running. Some insights and challenges relating to gait families, leg design, scaling, and out of plane motions for these running robots will be discussed.

Globally Optimal Gait Transition Policies for Compliant Bipedal Systems

By: William Martin (Hartmut Geyer)

The spring mass model provides a unified template for both running and walking on bipedal systems. Gait transition policies for this model are often designed by solving an optimization problem simplified with heuristics. These heuristics involve decisions on which parameters are allowed to vary at predefined points in the gait cycle. We extend this approach by searching for gait transition controllers with continuously variable leg stiffness throughout each stance phase. The generated policies are globally optimal and are used to study the limits of general bipedal gait transitions, without restricting the model to linear spring force profiles. In this talk we explore the robustness of these policies and hypothesize about the fundamental rules which govern them.