An omnidirectional closed-loop gait based on the direct feedback of orientation deviation estimates is presented in this paper. At the core of the gait is an open-loop central pattern generator. The orientation feedback is derived from a 3D nonlinear attitude estimator, and split into the relevant angular deviations in the sagittal and lateral planes using the concept of fused angles. These angular deviations from expected are used by a number of independent feedback mechanisms, including one that controls timing, to perform stabilising corrective actions. The tuning of the feedback mechanisms is discussed, including an LQR-based approach for tuning the transient sagittal response. The actuator control scheme and robot pose representations in use are also addressed. Experimental results on an igus® Humanoid Open Platform demonstrate the core concept of this paper, that if the sensor management and feedback chains are carefully constructed, comparatively simple model-free and robot-agnostic feedback mechanisms can successfully stabilise a generic bipedal gait.
When a disturbance to a stationary robot is detected, @cite_15 optimise two future footstep locations and one footstep time. The associated CoM trajectories are calculated explicitly using singular LQ preview regulation, based on the corresponding heuristically generated ZMP reference. The executed motion plan is fixed to always consist of exactly three steps, but this is sufficient to produce convincing disturbance rejection, albeit on specially designed hardware that is able to execute the planned motions with high fidelity.
@cite_15
2569324215 2015149365 2610901891 2172037318
In this paper, we present a convex optimization problem to generate Center of Mass (CoM) and momentum trajectories of a walking robot, such that the motion robustly satisfies the friction cone constraints on uneven terrain. We adopt the Contact Wrench Cone (CWC) criterion to measure a robot's dynamical stability, which generalizes the venerable Zero Moment Point (ZMP) criterion. Unlike the ZMP criterion, which is ideal for walking on flat ground with unbounded tangential friction forces, the CWC criterion incorporates non-coplanar contacts with friction cone constraints. We measure the robustness of the motion using the margin in the Contact Wrench Cone at each time instance, which quantifies the capability of the robot to instantaneously resist external force torque disturbance, without causing the foot to tip over or slide. For pre-specified footstep location and time, we formulate a convex optimization problem to search for robot linear and angular momenta that satisfy the CWC criterion. We aim to maximize the CWC margin to improve the robustness of the motion, and minimize the centroidal angular momentum (angular momentum about CoM) to make the motion natural. Instead of directly minimizing the non-convex centroidal angular momentum, we resort to minimizing a convex upper bound. We show that our CWC planner can generate motion similar to the result of the ZMP planner on flat ground with sufficient friction. Moreover, on an uneven terrain course with friction cone constraints, our CWC planner can still find feasible motion, while the outcome of the ZMP planner violates the friction limit. We present a new method for planning footstep placements for a robot walking on uneven terrain with obstacles, using a mixed-integer quadratically-constrained quadratic program (MIQCQP). Our approach is unique in that it handles obstacle avoidance, kinematic reachability, and rotation of footstep placements, which typically have required non-convex constraints, in a single mixed-integer optimization that can be efficiently solved to its global optimum. Reachability is enforced through a convex inner approximation of the reachable space for the robot's feet. Rotation of the footsteps is handled by a piecewise linear approximation of sine and cosine, designed to ensure that the approximation never overestimates the robot's reachability. Obstacle avoidance is ensured by decomposing the environment into convex regions of obstacle-free configuration space and assigning each footstep to one such safe region. We demonstrate this technique in simple 2D and 3D environments and with real environments sensed by a humanoid robot. We also discuss computational performance of the algorithm, which is currently capable of planning short sequences of a few steps in under one second or longer sequences of 10–30 footsteps in tens of seconds to minutes on common laptop computer hardware. Our implementation is available within the Drake MATLAB toolbox [1]. 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. We present a search-based planning approach for controlling a quadrupedal robot over rough terrain. Given a start and goal position, we consider the problem of generating a complete joint trajectory that will result in the legged robot successfully moving from the start to the goal. We decompose the problem into two main phases: an initial global planning phase, which results in a footstep trajectory; and an execution phase, which dynamically generates a joint trajectory to best execute the footstep trajectory. We show how R* search can be employed to generate high-quality global plans in the high-dimensional space of footstep trajectories. Results show that the global plans coupled with the joint controller result in a system robust enough to deal with a variety of terrains.