Many methods exist for a bipedal robot to keep its balance while walking. In addition to step size and timing, other strategies are possible that influence the stability of the robot without interfering with the target direction and speed of locomotion. This paper introduces a multifaceted feedback controller that uses numerous different feedback mechanisms, collectively termed corrective actions, to stabilise a core keypoint-based gait. The feedback controller is experimentally effective, yet free of any physical model of the robot, very computationally inexpensive, and requires only a single 6-axis IMU sensor. Due to these low requirements, the approach is deemed to be highly portable between robots, and was specifically also designed to target lower cost robots that have suboptimal sensing, actuation and computational resources. The IMU data is used to estimate the yaw-independent tilt orientation of the robot, expressed in the so-called tilt phase space, and is the source of all feedback provided by the controller. Experimental validation is performed in simulation as well as on real robot hardware.
We present a biped walking pattern generation based on a new way of system discretization named spatially quantized dynamics (SQD). In SQD, a continuous system is discretized by a constant unit length along the walk direction, and the dynamics is represented by a recurrence formula for a unit length motion, taking variable period for each cycle. Using SQD modelling, we can generate a biped gait by taking three steps;1)Design a walking pattern only considering kinematics in the sagittal plane, 2) Calculate the ZMP and velocity by optimization of the spatially quantized dynamics, 3) Add hip lateral motion for 3D dynamic balance. It is shown that we can easily generate a biped gait with stretched knees and a gait for large step climbing. The validity of the generated patterns are confirmed by simulations. We introduce a new method of a biped walking pattern generation by using a preview control of the zero-moment point (ZMP). First, the dynamics of a biped robot is modeled as a running cart on a table which gives a convenient representation to treat ZMP. After reviewing conventional methods of ZMP based pattern generation, we formalize the problem as the design of a ZMP tracking servo controller. It is shown that we can realize such controller by adopting the preview control theory that uses the future reference. It is also shown that a preview controller can be used to compensate the ZMP error caused by the difference between a simple model and the precise multibody model. The effectiveness of the proposed method is demonstrated by a simulation of walking on spiral stairs. We present an optimization based real-time walking controller for a full size humanoid robot. The controller consists of two levels of optimization, a high level trajectory optimizer that reasons about center of mass and swing foot trajectories, and a low level controller that tracks those trajectories by solving a floating base full body inverse dynamics problem using Quadratic Programming. Our controller is capable of walking on rough terrain, and also achieves longer foot steps, faster walking speed, heel-strike and toe push-off. Results are demonstrated with Boston Dynamics' Atlas robot in simulation. A humanoid walking robot is a highly nonlinear dynamical system that relies strongly on contact forces between its feet and the ground in order to realize stable motions, but these contact forces are unfortunately severely limited. Model predictive control, also known as receding horizon control, is a general control scheme specifically designed to deal with such constrained dynamical systems, with the potential ability to react efficiently to a wide range of situations. Apart from the question of computation time which needs to be taken care of carefully (these schemes can be highly computation intensive), the initial question of which optimal control problems should be considered to be solved online in order to lead to the desired walking movements is still unanswered. A key idea for answering to this problem can be found in the ZMP preview control scheme. After presenting here this scheme with a point of view slightly different from the original one, we focus on the problem of compensating strong perturbations of the dynamics of the robot and propose a new linear model predictive control scheme which is an improvement of the original ZMP preview control scheme. Here we present a closed-form solution to the continuous time-varying linear-quadratic regulator problem for zero-moment point (ZMP) tracking. This generalizes previous analytical solutions for gait generation by allowing "soft" tracking (with a quadratic cost) of the desired ZMP, and by providing the feedback gains for the resulting time-varying optimal controller. This enables very fast O(n) computation, with n the number of piecewise polynomial segments in the desired ZMP trajectory. Results are presented using the Atlas humanoid robot where dynamic walking is achieved by recomputing the optimal controller online. In this paper, we introduce an online decision method of foot placement for legged robots that manages unknown external forces. It consists of a fast trajectory generation method and an optimization method of foot placement. The fast trajectory generation method is based on an explicit solution for singular LQ preview regulation problem of an inverted pendulum model. By using the regulator problem, the conditions of target ZMP trajectory that will not make the COM trajectory diverge and a fast generation method of the COM trajectory which satisfies the target ZMP trajectory are obtained. An online optimization of foot placement is realized by using the fast trajectory generation method. An experiment of the online decision method of foot placement that manages unknown external force shows the performance of the proposed method.