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.
Many different approaches to the stabilisation of bipedal walking can be found in literature. Methods that are effective in actively rejecting large disturbances, yet do not use a physical model and only use a single inertial measurement unit (IMU) for feedback, are however infrequently encountered. A large proportion of walking methods, especially those for stiffer and higher quality robots, depend on zero-moment point (ZMP) based gait generation and or feedback. Usually this involves optimising for a future centre of mass (CoM) trajectory based on certain targets and constraints, and then trying to execute this as closely as possible with a lower level controller. Examples of this include in the settings of model predictive control @cite_10 , preview control @cite_6 @cite_11 , and an indirect generalisation in the form of differential dynamic programming (DDP) @cite_2 . @cite_12 also proposed a closed-form solution to the full continuous-time ZMP LQR problem over large horizons, while @cite_13 use spatially quantised dynamics (SQD), as opposed to temporal quantisation, with a mix of reference ZMP trajectory generation and divergent component of motion (DCM) dynamics to generate a gait that was able to utilise fully stretched knees.
@cite_13 @cite_6 @cite_2 @cite_10 @cite_12 @cite_11
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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. 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. This paper introduces an optimization-based framework for robust multilegged walking motion planning. Previous approaches use fixed gait sequences, and rely on Zero Moment Point (ZMP) to guarantee dynamic stability. While this combination works well on flat ground, it does not generalize to uneven terrain requiring aggressive gait or gait transition. To overcome such difficulties, in this paper, we present an optimization framework, that can plan both the contact location and gait sequence simultaneously in a mixed-integer convex optimization program. Moreover, we rely on the Contact Wrench Cone (CWC) stability criterion, which generalizes the ZMP criterion to uneven terrain with friction cone constraints, and we plan the walking motion together with the angular momentum through a convex optimization program. Our approach is successfully tested on a LittleDog quadruped over simulated scenarios. We show that on the flat ground, our planner generates a periodic gait, same as Central Pattern Generator + ZMP planner; while on uneven terrain, our planner can successfully generate a motion containing different gaits, with a center-of-mass motion that respects the friction cone constraints, which are violated by ZMP planners. This improvement clearly demonstrates the advantage of our approach over traditional planning strategies. 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.