Gait Generation and Optimization for Legged Robots

This paper presents a general framework for representing and generating gaitsfor legged robots. We introduce a convenient parametrization of gait generators as dynamical systems possessing specified stable limit cycles over an appropriate torus. Inspired by biology, this parametrization affords a continuous selection of operation within a coordination design plane spanned by axes that determine the mix of ”feedforward/feedback” and centralized/decentralized” control. Applying optimization to the parameterized gait generation system allowed RHex, our robotic hexapod, to learn new gaits demonstrating significant performance increases. For example, RHex can now run at 2.4m/s (up from 0.8m/s), run with a specific resistance of 0.6 (down from 2.0), climb 45◦ inclines (up from 25◦), and traverse 35◦ inclines (up from 15◦)

A novel approach to gait synchronization and transition for reconfigurable walking platforms

Legged robots based on one degree-of-freedom reconfigurable planar leg mechanisms, that are capable of generating multiple useful gaits, are highly desired due to the possibility of handling environments and tasks of high complexity while maintaining simple control schemes. An essential consideration in these reconfigurable legged robots is to attain stability in motion, at rest as well as while transforming from one configuration to another with the minimum number of legs as long as the full range of their walking patterns, resulting from the different gait cycles of their legs, is achieved. To this end, in this paper, we present a method for the generation of input joint trajectories to properly synchronize the movement of quadruped robots with reconfigurable legs. The approach is exemplified in a four-legged robot with reconfigurable Jansen legs capable of generating up to six useful different gait cycles. The proposed technique is validated through simulated results that show the platform׳s stability across its six feasible walking patterns and during gait transition phases, thus considerably extending the capabilities of the non-reconfigurable design

Multiple chaotic central pattern generators with learning for legged locomotion and malfunction compensation

An originally chaotic system can be controlled into various periodic dynamics. When it is implemented into a legged robot's locomotion control as a central pattern generator (CPG), sophisticated gait patterns arise so that the robot can perform various walking behaviors. However, such a single chaotic CPG controller has difficulties dealing with leg malfunction. Specifically, in the scenarios presented here, its movement permanently deviates from the desired trajectory. To address this problem, we extend the single chaotic CPG to multiple CPGs with learning. The learning mechanism is based on a simulated annealing algorithm. In a normal situation, the CPGs synchronize and their dynamics are identical. With leg malfunction or disability, the CPGs lose synchronization leading to independent dynamics. In this case, the learning mechanism is applied to automatically adjust the remaining legs' oscillation frequencies so that the robot adapts its locomotion to deal with the malfunction. As a consequence, the trajectory produced by the multiple chaotic CPGs resembles the original trajectory far better than the one produced by only a single CPG. The performance of the system is evaluated first in a physical simulation of a quadruped as well as a hexapod robot and finally in a real six-legged walking machine called AMOSII. The experimental results presented here reveal that using multiple CPGs with learning is an effective approach for adaptive locomotion generation where, for instance, different body parts have to perform independent movements for malfunction compensation.Comment: 48 pages, 16 figures, Information Sciences 201

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

Frequency-Aware Model Predictive Control

Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion infeasible on the real system. Model errors can be a result of model simplifications, but also naturally arise when deploying the robot in unstructured and nondeterministic environments. Predominantly, compliant contacts and actuator dynamics lead to bandwidth limitations. While classical control methods provide tools to synthesize controllers that are robust to a class of model errors, such a notion is missing in modern trajectory optimization, which is solved in the time domain. We propose frequency-shaped cost functions to achieve robust solutions in the context of optimal control for legged robots. Through simulation and hardware experiments we show that motion plans can be made compatible with bandwidth limits set by actuators and contact dynamics. The smoothness of the model predictive solutions can be continuously tuned without compromising the feasibility of the problem. Experiments with the quadrupedal robot ANYmal, which is driven by highly-compliant series elastic actuators, showed significantly improved tracking performance of the planned motion, torque, and force trajectories and enabled the machine to walk robustly on terrain with unmodeled compliance