Shishir Kolathaya

Dynamic multi-domain bipedal walking with atrias through SLIP based human-inspired control

This paper presents a methodology for achieving efficient multi-domain underactuated bipedal walking on compliant robots by formally emulating gaits produced by the Spring Loaded Inverted Pendulum (SLIP). With the goal of achieving locomotion that displays phases of double and single support, a hybrid system model is formulated that faithfully represents the full-order dynamics of a compliant walking robot. The SLIP model is used as a bases for constructing human-inspired controllers that yield a dimension reduction through the use of hybrid zero dynamics. This allows for the formulation of an optimization problem that produces hybrid zero dynamics that best represents a SLIP model walking gait, while simultaneously ensuring the proper reduction in dimensionality that can be utilized to produce stable periodic orbits, i.e., walking gaits. The end result is stable robotic walking in simulation and, when implemented on the compliant robot ATRIAS, experimentally realized dynamic multi-domain locomotion.

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.

Achieving bipedal locomotion on rough terrain through human-inspired control

This paper presents a method for achieving robotic walking on rough terrain through Human-Inspired Control. This control methodology uses human data to achieve human like walking in robots by considering outputs that appear to be indicative of walking, and using nonlinear control methods to track a set of functions called Canonical Walking Functions (CWF). While this method has proven successful on a specific well-defined terrain, rough terrain walking is achieved by dynamically changing the CWF that the robot outputs should track at every step. To make the computation more tractable Extended Canonical Walking Functions (ECWF) are used to generate these desired functions instead of CWF. The state of the robot, after every non-stance foot strike, is actively sensed and a new CWF is constructed to ensure Hybrid Zero Dynamics is respected for the next step. Finally, the technique developed is implemented on different terrains in simulation. The same technique is adopted experimentally on the bipedal robot AMBER and tested on sinusoidal terrain. Experimental results show how the walking gait morphs based upon the terrain, thereby justifying the theory applied.

Quadratic programming and impedance control for transfemoral prosthesis.

This paper presents a novel optimal control strategy combining control Lyapunov function (CLF) based quadratic programs with impedance control, with the goal of improving both tracking performance and the stability of controllers implemented on transfemoral prosthesis. CLF based quadratic programs have the inherent capacity to optimally track a desired trajectory. This property is used in congruence with impedance control - implemented as a feedforward term - to realize significantly small tracking errors, while simultaneously yielding bipedal walking that is both stable and robust to disturbances. Moreover, instead of experimentally validating this on human subjects, a virtual prosthesis is attached to a robotic testbed, AMBER. The authors claim that the walking of AMBER is human like and therefore form a suitable substitute to human subjects on which a prosthetic control can be tested. Based on this idea, the proposed controller was first verified in simulation, then tested on the physical robot AMBER. The results indicate improved tracking performance, stability, and robustness to unknown disturbances.

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.

Time dependent control Lyapunov functions and hybrid zero dynamics for stable robotic locomotion

Implementing state-based parameterized periodic trajectories on complex robotic systems, e.g., humanoid robots, can lead to instability due to sensor noise exacerbated by dynamic movements. As a means of understanding this phenomenon, and motivated by field testing on the humanoid robot DURUS, this paper presents sufficient conditions for the boundedness of hybrid periodic orbits (i.e., boundedness of walking gaits) for time dependent control Lyapunov functions. In particular, this paper considers virtual constraints that yield hybrid zero dynamics with desired outputs that are a function of time or a state-based phase variable. If the difference between the phase variable and time is bounded, we establish exponential boundedness to the zero dynamics surface. These results are extended to hybrid dynamical systems, establishing exponential boundedness of hybrid periodic orbits, i.e., we show that stable walking can be achieved through time-based implementations of state-based virtual constraints. These results are verified on the bipedal humanoid robot DURUS both in simulation and experimentally; it is demonstrated that a close match between time based tracking and state based tracking can be achieved as long as there is a close match between the time and phase based desired output trajectories.

Parameter Sensitivity and Boundedness of Robotic Hybrid Periodic Orbits

Abstract Model-based nonlinear controllers like feedback linearization and control Lyapunov functions are highly sensitive to the model parameters of the robot. This paper addresses the problem of realizing these controllers in a particular class of hybrid models-systems with impulse effects-through a parameter sensitivity measure. This measure quantifies the sensitivity of a given model-based controller to parameter uncertainty along a particular trajectory By using this measure, output boundedness of the controller (computed torque+PD) will be analyzed. Given outputs that characterize the control objectives, i.e., the goal is to drive these outputs to zero, we consider Lyapunov functions obtained from these outputs. The main result of this paper establishes the ultimate boundedness of the output dynamics in terms of this measure via these Lyapunov functions under the assumption of stable hybrid zero dynamics. This is demonstrated in simulation on a 5-DOF underactuated bipedal robot.

Online optimal gait generation for bipedal walking robots using legendre pseudospectral optimization

This paper presents an optimal gait synthesis method that exploits the full body dynamics of robots using the Hybrid Zero Dynamics (HZD) control framework and-for the first time-experimentally realizes online HZD gait generation for a planar underactuated robot. Hybrid zero dynamics is an established theoretical framework that formally enables stable control of dynamic locomotion by enforcing virtual constraints through feedback controllers. An essential part of successfully realizing dynamic walking with HZD framework is determining parameters of the virtual constraints that satisfy hybrid invariant condition via nonlinear constrained optimization. Due to the complexity of the full hybrid system model of the robot, these optimization problems often suffer from slow convergence and local minima. In this paper, we improve the reliability of the HZD gait optimization and significantly increase the convergence speed by taking advantage of the direct transcription formulation and the exponential convergence of the global orthogonal collocation (a.k.a. pseudospectral) method. As a result, generating HZD gaits online becomes feasible with an average computation time less than 0.5 seconds, as will be demonstrated experimentally on a bipedal robot.

Exponential convergence of a unified CLF controller for robotic systems under parameter uncertainty

This paper presents a novel method for achieving exponential convergence of a Control Lyapunov Function (CLF) based controller in a n-DOF robotic system in the presence of parameter uncertainty. Utilizing the linearity of parameters in the equations of motion, we construct the regressor and augment the state space of the robot to include a vector of unknown parameters, called base inertial parameters. The augmented state space can be utilized to realize an optimal controller that is exponentially stable while simultaneously estimating the parameters online. To achieve this result, acceleration data for a given torque input is measured and used to compute the regressor. This, in turn, is used to compute the set of base inertial parameters in the form of linear equality constraints. By demonstrating that it is not necessary for the estimated parameters to converge to the actual parameters, but rather convergence is only needed on a specified space, we are able to construct a quadratic program enforcing convergence. The end result is that exponential convergence of a Control Lyapunov Function can be guaranteed, in an optimal fashion, without prior knowledge of the parameters.