Wen-Loong Ma

Human-Inspired Multi-Contact Locomotion with AMBER2

This paper presents a methodology for translating a key feature encoded in human locomotion - multi-contact behavior - to a physical 2D bipedal robot, AMBER2, by leveraging novel controller design, optimization methods, and software structures for the translation to hardware. This paper begins with the analysis of human locomotion data and uses it to motivate the construction of a hybrid system model representing a multi-contact robotic walking gait. By again looking to human data for inspiration, human-inspired controllers are developed and used in the formulation of an optimization problem that yields stable human-like multi-domain walking in simulation. These formal results are translated to hardware implementation via a novel dynamic trajectory generation strategy. Finally, the specific software structures utilized to translate these trajectories to hardware are presented. The end result is experimentally realized stable robotic walking with remarkably human-like multi-contact foot behaviors.

Human-inspired walking via unified PD and impedance control.

This paper describes a torque control scheme unifying feedback PD control and feed-forward impedance control to realize human-inspired walking on a novel planar footed bipedal robot: AMBER2. It starts with high fidelity modeling of the robot including nonlinear dynamics, motor model, and impact dynamics. Human data is then used by an optimization algorithm to produce a human-like gait that can be implemented on the robot. To realize the bipedal walking, first a PD controller is utilized to track the optimized trajectory. Next, impedance control parameters are estimated from the experimental data. Finally, the unified PD, impedance torque control law is experimentally realized on the bipedal robot AMBER2. Through the evidence of sustainable and unsupported walking on AMBER2 showing high consistency with the simulated gait, the feasibility of AMBER2 walking scheme will be verified.

Adaptive cruise control: Experimental validation of advanced controllers on scale-model cars

Recent advances in automotive technology, such as, sensing and onboard computation, have resulted in the development of adaptive cruise control (ACC) algorithms that improve both comfort and safety. With a view towards developing advanced controllers for ACC, this paper presents an experimental platform for validation and demonstration of an online optimization based controller. Going beyond traditional PID based controllers for ACC that lack proof of safety, we construct a control framework that gives formal guarantees of correctness. In particular, safety constraints-maintaining a valid following distance from a lead car-are represented by control barrier functions (CBFs), and control objectives- achieving a desired speed-are encoded through control Lyapunov functions (CLFs). These different objectives can be unified through a quadtraic program (QP), with constraints dictated by CBFs and CLFs, that balances safety and the control objectives in an optimal fashion. This methodology is demonstrated on scale-model cars, for which the CBF-CLF based controller is implemented online, with the end result being the experimental validation of an advanced adaptive cruise controller.

Multi-Contact Bipedal Robotic Locomotion

This paper presents a formal framework for achieving multi-contact bipedal robotic walking, and realizes this methodology experimentally on two robotic platforms: AMBER2 and Assume The Robot Is A Sphere (ATRIAS). Inspired by the key feature encoded in human walking—multi-contact behavior—this approach begins with the analysis of human locomotion and uses it to motivate the construction of a hybrid system model representing a multi-contact robotic walking gait. Human-inspired outputs are extracted from reference locomotion data to characterize the human model or the spring-loaded invert pendulum (SLIP) model, and then employed to develop the human-inspired control and an optimization problem that yields stable multi-domain walking. Through a trajectory reconstruction strategy motivated by the process that generates the walking gait, the mathematical constructions are successfully translated to the two physical robots experimentally.

First steps toward formal controller synthesis for bipedal robots

Bipedal robots are prime examples of complex cyber-physical systems (CPS). They exhibit many of the features that make the design and verification of CPS so difficult: hybrid dynamics, large continuous dynamics in each mode (e.g., 10 or more state variables), and nontrivial specifications involving nonlinear constraints on the state variables. In this paper, we propose a two-step approach to formally synthesize control software for bipedal robots so as to enforce specifications by design and thereby generate physically realizable stable walking. In the first step, we design outputs and classical controllers driving these outputs to zero. The resulting controlled system evolves on a lower dimensional manifold and is described by the hybrid zero dynamics governing the remaining degrees of freedom. In the second step, we construct an abstraction of the hybrid zero dynamics that is used to synthesize a controller enforcing the desired specifications to be satisfied on the full order model. Our two step approach is a systematic way to mitigate the curse of dimensionality that hampers the applicability of formal synthesis techniques to complex CPS. Our results are illustrated with simulations showing how the synthesized controller enforces all the desired specifications and offers improved performance with respect to a controller that was utilized to obtain walking experimentally on the bipedal robot AMBER 2.

Bipedal Robotic Running with DURUS-2D: Bridging the Gap between Theory and Experiment

Bipedal robotic running remains a challenging benchmark in the field of control and robotics because of its highly dynamic nature and necessarily underactuated hybrid dynamics. Previous results have achieved bipedal running experimentally with a combination of theoretical results and heuristic application thereof. In particular, formal analysis of the hybrid system stability is given based on a theoretical model, but due to the gap between theoretical concepts and experimental reality, extensive tuning is necessary to achieve experimental success. In this paper, we present a formal approach to bridge this gap, starting from theoretical gait generation to a provably stable control implementation, resulting in bipedal robotic running. We first use a large-scale optimization to generate an energy-efficient running gait, subject to hybrid zero dynamics conditions and feasibility constraints which incorporate practical limitations of the robot model based on physical conditions. The stability of the gait is formally guaranteed in the hybrid system model with an input to state stability (ISS) based control law. This implementation improves the stability under practical control limitations of the system. Finally, the methodology is experimentally realized on the planar spring-legged bipedal robot, DURUS-2D, resulting in sustainable running at 1.75m/s. The paper, therefore, presents a formal method that takes the first step toward bridging the gap between theory and experiment.

Corrigendum: Multi-contact bipedal robotic locomotion

In Eq. (22), the x symbol was incorrectly represented by an @ symbol, therefore the equation should correctly read as \begin{eqnarray*} \dot x &=& {f_v}(x) + {g_v}(x)u,\\ {y_v} &=& y_v^a(x) - y_v^d(x). \end{eqnarray*} Similar errors were also found in the sentence following Eq. (22). In this sentence, the correct math symbol should be y v a ( x ) and y v d ( x ) instead of y v a (@) and y v d (@).

Toward benchmarking locomotion economy across design configurations on the modular robot: AMBER-3M

Making conclusive performance comparisons of bipedal locomotion behaviors can be difficult when working with different robots. This is particularly true in the case of comparing energy economy, which is highly dependent on mechanical, electrical and control components. As a means of limiting these disparities in methodical testing, we built a modular bipedal robot platform, AMBER-3M. Three leg configurations were designed for this purpose: actuated flat foot, rigid point-foot, and compliant point-foot. As a proof of concept for the mechanical, electrical, and algorithmic modularity, we present walking experiments with all three AMBER-3M configurations, using the same control methods and experimental procedures. As a pilot study for investigating locomotion economy, we performed further systematic experiments of point-foot walking with the purpose of examining the effects of speed on the cost of transport (COT). We optimized 36 walking gaits for maximum locomotion economy at various transport velocities. Walking performance data was collected from these gaits spanning a speed range of 0.34 to 0.94m/s. An apparent Pareto-optimal frontier was observed in the data, showing that mechanical cost of transport increases with speed; ranging from 0.22 up to 0.36. Conversely, the electrical cost of transport decreased at higher walking speeds.

Composing Dynamical Systems to Realize Dynamic Robotic Dancing

This paper presents a methodology for the composition of complex dynamic behaviors in legged robots, and illustrates these concepts to experimentally achieve robotic dancing . Inspired by principles from dynamic locomotion, we begin by constructing controllers that drive a collection of virtual constraints to zero; this creates a low-dimensional representation of the bipedal robot. Given any two poses of the robot, we utilize this low-dimensional representation to connect these poses through a dynamic transition. The end result is a meta-dynamical system that describes a series of poses (indexed by the vertices of a graph) together with dynamic transitions (indexed by the edges) connecting these poses. These formalisms are illustrated in the case of dynamic dancing; a collection of ten poses are connected through dynamic transitions obtained via virtual constraints, and transitions through the graph are synchronized with music tempo. The resulting meta-dynamical system is realized experimentally on the bipedal robot AMBER 2 yielding dynamic robotic dancing.