This paper presents a hierarchical control strategy based on hybrid systems theory, nonlinear control, and safety-critical systems to enable cooperative locomotion of robotic guide dogs and visually impaired people. We address high-dimensional and complex hybrid dynamical models that represent collaborative locomotion. At the high level of the control scheme, local and nonlinear baseline controllers, based on the virtual constraints approach, are designed to induce exponentially stable dynamic gaits. The baseline controller for the leash is assumed to be a nonlinear controller that keeps the human in a safe distance from the dog while following it. At the lower level, a real-time quadratic programming (QP) is solved for modifying the baseline controllers of the robot as well as the leash to avoid obstacles. In particular, the QP framework is set up based on control barrier functions (CBFs) to compute optimal control inputs that guarantee safety while being close to the baseline controllers. The stability of the complex periodic gaits is investigated through the Poincare return map. To demonstrate the power of the analytical foundation, the control algorithms are transferred into an extensive numerical simulation of a complex model that represents cooperative locomotion of a quadrupedal robot, referred to as Vision 60, and a human model. The complex model has 16 continuous-time domains with 60 state variables and 20 control inputs.
 This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3-D bipedal robot consisting of a torso, revolute knees, and passive (unactuated) point feet. The walking surface is assumed to be rigid and flat; the contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and six actuators. In addition to the reduced number of actuators, the interest of studying robots with point feet is that the feedback control solution must explicitly account for the robot's natural dynamics in order to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics (HZD), a very successful method for planar bipeds, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit, for a 3-D (spatial) bipedal walking robot. This method allows the computations for the controller design and the periodic orbit to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincare map of the HZD. Most periodic walking gaits for this robot are unstable when the controlled outputs are selected to be the actuated coordinates. Three strategies are explored to produce stable walking. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an event-based controller to modify the eigenvalues of the (linearized) Poincare map. In the third approach, the effect of output selection on the zero dynamics is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller.    While legged animals are adept at traversing rough landscapes, it remains a very challenging task for a legged robot to negotiate unknown terrain. Control systems for legged robots are plagued by dynamic constraints from underactuation, actuator power limits, and frictional ground contact; rather than relying purely on disturbance rejection, considerable advantage can be obtained by planning nominal trajectories which are more easily stabilized. In this paper, we present an approach for designing nominal periodic trajectories for legged robots that maximize a measure of robustness against uncertainty in the geometry of the terrain. We propose a direct collocation method which solves simultaneously for a nominal periodic control input, for many possible one-step solution trajectories (using ground profiles drawn from a distribution over terrain), and for the periodic solution to a jump Riccati equation which provides an expected infinite-horizon cost-to-go for each of these samples. We demonstrate that this trajectory optimization scheme can recover the known deadbeat open-loop control solution for the Spring Loaded Inverted Pendulum (SLIP) on unknown terrain. Moreover, we demonstrate that it generalizes to other models like the bipedal compass gait walker, resulting in a dramatic increase in the number of steps taken over moderate terrain when compared against a limit cycle optimized for efficiency only.  The purpose of this paper is to apply methods from geometric mechanics to the analysis and control of bipedal robotic walkers. We begin by introducing a generalization of Routhian reduction, functional Routhian Reduction, which allows for the conserved quantities to be functions of the cyclic variables rather than constants. Since bipedal robotic walkers are naturally modeled as hybrid systems, which are inherently nonsmooth, in order to apply this framework to these systems it is necessary to first extend functional Routhian reduction to a hybrid setting. We apply this extension, along with potential shaping and controlled symmetries, to derive a feedback control law that provably results in walking gaits on flat ground for a three-dimensional bipedal walker given walking gaits in two dimensions. While the goal of robotic bipedal walking to date has been the development of anthropomorphic gait, the community as a whole has been unable to agree upon an appropriate model to generate such gait. In this paper, we describe a method to segment human walking data in order to generate a robotic model capable of human-like walking. Generating the model requires the determination of the sequence of contact point enforcements which requires solving a combinatorial scheduling problem. We resolve this problem by transforming the detection of contact point enforcements into a constrained switched system optimal control problem for which we develop a provably convergent algorithm. We conclude the paper by illustrating the performance of the algorithm on identifying a model for robotic bipedal walking.  Navigation in pedestrian environments is critical to enabling independent mobility for the blind and visually impaired (BVI) in their daily lives. White canes have been commonly used to obtain contact feedback for following walls, curbs, or man-made trails, whereas guide dogs can assist in avoiding physical contact with obstacles or other pedestrians. However, the infrastructures of tactile trails or guide dogs are expensive to maintain. Inspired by the autonomous lane following of self-driving cars, we wished to combine the capabilities of existing navigation solutions for BVI users. We proposed an autonomous, trail-following robotic guide dog that would be robust to variances of background textures, illuminations, and interclass trail variations. A deep convolutional neural network (CNN) is trained from both the virtual and realworld environments. Our work included major contributions: 1) conducting experiments to verify that the performance of our models trained in virtual worlds was comparable to that of models trained in the real world; 2) conducting user studies with 10 blind users to verify that the proposed robotic guide dog could effectively assist them in reliably following man-made trails. Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations can lead to conflicting and even paradoxical results. As robotics modeling moves from the consideration of isolated behaviors to the analysis of tasks requiring their composition, a mathematically tractable framework for building models that combine these simple approximations yet achieve reliable results is overdue. In this paper we present a formal hybrid dynamical system model that introduces suitably restricted compositions of these familiar abstractions with the guarantee of consistency analogous to global existence and uniqueness in classical dynamical systems. The hybrid system developed here provides a discontinuous but self-consistent approximation to the continuous though possibly very stiff and fast dynamics of a physical robot undergoing intermittent impacts. The modeling choices sacrifice some quantitative numerical efficiencies while maintaining qualitatively correct and analytically tractable results with consistency guarantees promoting their use in formal reasoning about mechanism, feedback control, and behavior design in robots that make and break contact with their environment. We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated âdynamic walkingâ biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not known in advance. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents âtransversalâ dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design, providing exponential orbital stability of the target trajectory of the original nonlinear system. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to a wide variety of hybrid nonlinear systems.   For an underactuated biped on a constant-slope terrain, the hybrid zero dynamics (HZD) controller framework provides exponentially stable walking motions. In this paper, we quantify the stability of such a control system on rough terrain by estimating the expected number of steps before failure. In addition, we show how to switch between multiple HZD controllers (optionally using terrain look-ahead) to increase the stability dramatically, e.g., 10 thousand steps compared to 10. To do this robustly, we make use of the new meshing method proposed in this paper. Hybrid zero dynamics (HZD) has emerged as a popular framework for dynamic walking but has significant implementation difficulties when applied to the high degrees of freedom humanoids. The primary impediment is the process of gait design—it is difficult for optimizers to converge on a viable set of virtual constraints defining a gait. This paper presents a methodology that allows for fast and reliable generation of dynamic robotic walking gaits through the HZD framework, even in the presence of underactuation. Specifically, we describe an optimization formulation that builds upon the novel combination of HZD and direct collocation methods. Furthermore, achieving a scalable implementation required developing a defect-variable substitution formulation to simplify expressions, which ultimately allows us to generate compact analytic Jacobians of the constraints. We experimentally validate our methodology on an underactuated humanoid, DURUS, a spring-legged machine designed to facilitate energy-economical walking. We show that the optimization approach, in concert with the HZD framework, yields dynamic and stable walking gaits in hardware with a total electrical cost of transport of 1.33. The GuideCane is a device designed to help blind or visually impaired users navigate safely and quickly among obstacles and other hazards. During operation, the user pushes the lightweight GuideCane forward. When the GuideCane's ultrasonic sensors detect an obstacle, the embedded computer determines a suitable direction of motion that steers the GuideCane and the user around it. The steering action results in a very noticeable force felt in the handle, which easily guides the user without any conscious effort on his her part.