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.
Although important theoretical and technological advances have occurred for the construction and control of guide robots, state-of-the-art approaches are mainly tailored to the deployment of wheeled vehicles and legged guide robots (e.g., @cite_23 @cite_33 @cite_17 ). Unlike wheeled guide robots, legged robots are complex dynamical systems with hybrid nature and high degrees of freedom (DOF). This complicates the design of feedback control algorithms that ensure stable and safe cooperative locomotion of guide dogs and human. Hybrid systems theory has become a powerful approach for modeling and control of legged robots both in theory and practice @cite_28 @cite_18 @cite_26 @cite_13 @cite_12 @cite_15 @cite_7 @cite_24 @cite_8 @cite_25 @cite_2 @cite_11 @cite_5 @cite_3 . Existing nonlinear control approaches that address the hybrid nature of legged locomotion models are developed based on hybrid reduction @cite_9 , controlled symmetries @cite_11 , transverse linearization @cite_5 , and hybrid zero dynamics (HZD) @cite_18 @cite_13 . State-of-the art nonlinear control approaches for dynamic legged locomotion have been tailored to stable locomotion of legged robots, but stable and safe cooperative locomotion of legged guide robots and visually impaired people.
@cite_18 @cite_26 @cite_11 @cite_33 @cite_7 @cite_8 @cite_28 @cite_9 @cite_3 @cite_24 @cite_23 @cite_2 @cite_5 @cite_15 @cite_13 @cite_25 @cite_12 @cite_17
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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. 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. Navigating in search and rescue environments is challenging, since a variety of terrains has to be considered. Hybrid driving-stepping locomotion, as provided by our robot Momaro, is a promising approach. Similar to other locomotion methods, it incorporates many degrees of freedom—offering high flexibility but making planning computationally expensive for larger environments. We propose a navigation planning method, which unifies different levels of representation in a single planner. In the vicinity of the robot, it provides plans with a fine resolution and a high robot state dimensionality. With increasing distance from the robot, plans become coarser and the robot state dimensionality decreases. We compensate this loss of information by enriching coarser representations with additional semantics. Experiments show that the proposed planner provides plans for large, challenging scenarios in feasible time.