Keep Rollin' - Whole-Body Motion Control and Planning for Wheeled Quadrupedal Robots

We show dynamic locomotion strategies for wheeled quadrupedal robots, which combine the advantages of both walking and driving. The developed optimization framework tightly integrates the additional degrees of freedom introduced by the wheels. Our approach relies on a zero-moment point based motion optimization which continuously updates reference trajectories. The reference motions are tracked by a hierarchical whole-body controller which computes optimal generalized accelerations and contact forces by solving a sequence of prioritized tasks including the nonholonomic rolling constraints. Our approach has been tested on ANYmal, a quadrupedal robot that is fully torque-controlled including the non-steerable wheels attached to its legs. We conducted experiments on flat and inclined terrains as well as over steps, whereby we show that integrating the wheels into the motion control and planning framework results in intuitive motion trajectories, which enable more robust and dynamic locomotion compared to other wheeled-legged robots. Moreover, with a speed of 4 m/s and a reduction of the cost of transport by 83 % we prove the superiority of wheeled-legged robots compared to their legged counterparts.Comment: IEEE Robotics and Automation Letter

Footstep and Motion Planning in Semi-unstructured Environments Using Randomized Possibility Graphs

Traversing environments with arbitrary obstacles poses significant challenges for bipedal robots. In some cases, whole body motions may be necessary to maneuver around an obstacle, but most existing footstep planners can only select from a discrete set of predetermined footstep actions; they are unable to utilize the continuum of whole body motion that is truly available to the robot platform. Existing motion planners that can utilize whole body motion tend to struggle with the complexity of large-scale problems. We introduce a planning method, called the "Randomized Possibility Graph", which uses high-level approximations of constraint manifolds to rapidly explore the "possibility" of actions, thereby allowing lower-level motion planners to be utilized more efficiently. We demonstrate simulations of the method working in a variety of semi-unstructured environments. In this context, "semi-unstructured" means the walkable terrain is flat and even, but there are arbitrary 3D obstacles throughout the environment which may need to be stepped over or maneuvered around using whole body motions.Comment: Accepted by IEEE International Conference on Robotics and Automation 201

Motion Planning of Legged Robots

We study the problem of computing the free space F of a simple legged robot called the spider robot. The body of this robot is a single point and the legs are attached to the body. The robot is subject to two constraints: each leg has a maximal extension R (accessibility constraint) and the body of the robot must lie above the convex hull of its feet (stability constraint). Moreover, the robot can only put its feet on some regions, called the foothold regions. The free space F is the set of positions of the body of the robot such that there exists a set of accessible footholds for which the robot is stable. We present an efficient algorithm that computes F in O(n2 log n) time using O(n2 alpha(n)) space for n discrete point footholds where alpha(n) is an extremely slowly growing function (alpha(n) <= 3 for any practical value of n). We also present an algorithm for computing F when the foothold regions are pairwise disjoint polygons with n edges in total. This algorithm computes F in O(n2 alpha8(n) log n) time using O(n2 alpha8(n)) space (alpha8(n) is also an extremely slowly growing function). These results are close to optimal since Omega(n2) is a lower bound for the size of F.Comment: 29 pages, 22 figures, prelininar results presented at WAFR94 and IEEE Robotics & Automation 9

Imprecise dynamic walking with time-projection control

We present a new walking foot-placement controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of the 3LP model, our proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. This control paradigm reacts to disturbances immediately and includes rules to account for swing dynamics and leg-retraction. We apply it to a simulated Atlas robot in position-control, always commanded to perform in-place walking. The stance hip joint in our robot keeps the torso upright to let the robot naturally fall, and the swing hip joint tracks the desired footstep location. Combined with simple Center of Pressure (CoP) damping rules in the low-level controller, our foot-placement enables the robot to recover from strong pushes and produce periodic walking gaits when subject to persistent sources of disturbance, externally or internally. These gaits are imprecise, i.e., emergent from asymmetry sources rather than precisely imposing a desired velocity to the robot. Also in extreme conditions, restricting linearity assumptions of the 3LP model are often violated, but the system remains robust in our simulations. An extensive analysis of closed-loop eigenvalues, viable regions and sensitivity to push timings further demonstrate the strengths of our simple controller

ZMP support areas for multi-contact mobility under frictional constraints

We propose a method for checking and enforcing multi-contact stability based on the Zero-tilting Moment Point (ZMP). The key to our development is the generalization of ZMP support areas to take into account (a) frictional constraints and (b) multiple non-coplanar contacts. We introduce and investigate two kinds of ZMP support areas. First, we characterize and provide a fast geometric construction for the support area generated by valid contact forces, with no other constraint on the robot motion. We call this set the full support area. Next, we consider the control of humanoid robots using the Linear Pendulum Mode (LPM). We observe that the constraints stemming from the LPM induce a shrinking of the support area, even for walking on horizontal floors. We propose an algorithm to compute the new area, which we call pendular support area. We show that, in the LPM, having the ZMP in the pendular support area is a necessary and sufficient condition for contact stability. Based on these developments, we implement a whole-body controller and generate feasible multi-contact motions where an HRP-4 humanoid locomotes in challenging multi-contact scenarios.Comment: 14 pages, 10 figure

Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on Robotics (2019