Hierarchical controller for highly dynamic locomotion utilizing pattern modulation and impedance control : implementation on the MIT Cheetah robot

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 105-111).This thesis presents a hierarchical control algorithm for quadrupedal locomotion. We address three challenges in developing a controller for high-speed running: locomotion stability, control of ground reaction force, and coordination of four limbs. To tackle these challenges, the proposed algorithm employs three strategies. Leg impedance control provides programmable virtual compliance of each leg which achieve self-stability in locomotion. The four legs exert forces to the ground using equilibrium-point hypothesis. A gait pattern modulator imposes a desired footfall sequence. The control algorithm is verified in a dynamic simulator constructed using MATLAB and then in the subsequent experiments on the MIT Cheetah robot. The experiments on the MIT Cheetah robot demonstrates high speed trot running reaching up to the speed of 6 m/s on a treadmill. This speed corresponds to a Froude number (Fr = 7.34), which is comparatively higher than other existing quadrupedal robots.by Jongwoo Lee.S.M

Investigation of an Articulated Spine in a Quadruped Robotic System.

This research quantitatively analyzes a multi-body dynamics quadrupedal model with an articulated spine to evaluate the effects of speed and stride frequency on the energy requirements of the system. The articulated model consists of six planar, rigid bodies with a single joint in the middle of the torso. All joints are frictionless and mass is equally distributed in the limbs and torso. A model with the mid-torso joint removed, denoted as the rigid model, is used as a baseline comparison. Impulsive forces and torques are used to instantaneously reset the velocities at the phase transitions, allowing for ballistic trajectories during flight phases. Active torques at the haunch and shoulder joints are used during the stance phases to increase the model robustness. Simulations were conducted over effective high-speed gaits from 6.0 - 9.0 m/s. Stride frequencies were varied for both models. An evolutionary algorithm was employed to find plausible gaits based on biologically realistic constraints and bounds. The objective function for the optimization was cost of transport. Results show a decreasing cost of transport as speed increases for the articulated model with an optimal stride frequency of 3 s$^{-1}$ and an increasing cost of transport with increasing speed for the rigid model at an optimal stride frequency of 1.4 s$^{-1}$, with a crossover in the cost of transport between the two models occurring at 7.0 m/s. The rigid model favors low speeds and stride frequencies at the cost of a large impulsive vertical force, driving the system through a long, gathered flight phase used to cover the long distances at the low stride frequencies. The articulated model prefers higher speeds and stride frequencies at the cost of a large impulsive torque in the back joint, akin to the contraction of abdomen muscles, preventing the collapse of the back. Thus, it is demonstrated that the inclusion of back articulation enables a more energetically efficient high-speed gait than a rigid back system, as seen in biological systems. Detailed analysis is provided to identify the mechanics associated with the optimal gaits of both the rigid and the articulated systems to support this claim.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89831/1/bhaueise_1.pd

Treadmill Platform for Quadrupedal Robots

Cal Poly Legged Robots, led by Professor Refvem and Professor Xing, has been leading Cal Poly’s attempts to simulate, produce, and test their legged robots. The initial testing of the locomotion of these robots can be dangerous to the robot since any bugs in the code could cause the robot to fall over and harm itself. Our responsibility as a team was to deliver a portable platform for testing the locomotion capabilities containing a fall prevention mechanism. In short, we have designed a platform for this purpose that consists of a treadmill surrounded by a wheeled chassis with a system of ropes, pulleys, and a winch for a fall prevention mechanism. Our method of lifting the robot is a success in two ways. First, our method only requires the addition of four eyebolts to the robot, a rather minor modification. Second, our method does not impede the motion of the robot when it is running normally. However, it was found that our method requires 1-1.7 seconds to lift the robot (depending on where the robot is located on the treadmill) – a rather crippling amount of time to lift a robot, seeing as how it is desired for the robot to run at 8 mph on the treadmill. Regardless, our design provides a great starting point for future Senior Project teams to improve upon it. It is our hope that our design will allow Cal Poly Legged Robots to further the development of legged robots and to generate interest, both at Cal Poly and hopefully around the world, in this area of study

ロボティクスのための深層強化学習による運動シナジー発現と冗長性定量化に関する研究

Tohoku University林部充宏課

Using learning algorithms to develop dynamic gaits for legged robots

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.Includes bibliographical references (p. 129-134).As more legged robots have begun to be developed for their obvious advantages in overall maneuverability and mobility over rough terrain and difficult obstacles, their shortcomings over flat terrain have become more apparent. These robots plod along at extremely low speeds even when the ground is flat and level due to the fact that virtually all legged robots use a very stable, very slow walking gait to move, regardless of whether the ground is flat or rough. The simplest way of solving this problem is to use the same method as legged animals: simply change the gait from a walk to a faster more dynamic gait in order to increase the robot's speed. It would be extremely useful if legged robots were capable of moving across flat ground at high velocities while still retaining their ability to cross extremely rough or broken ground. Unfortunately, dynamic gaits are quite difficult to program by hand and only minimal research has been done on them. This thesis evaluates the use of two different types of learning algorithms (a genetic algorithm and a modified gradient-climbing reinforcement learning algorithm) as applied to the problem of developing dynamic gaits for a simulation of the Sony Aibo robot.(cont.) The two algorithms are tested using a random starting population and a high-fitness starting population and the results from both tests are compared. The research focuses on three different types of dynamic gaits: the trot, the canter, and the gallop. The efficiencies of the learned gaits are compared to each other in order to try to determine the best type of high-speed gait for use on the Aibo robot. Problems with the design of the Aibo robot as related to performing dynamic gaits are also identified and solutions are proposed.by Brian Schaaf.S.M

Stride-level control of quadrupedal runners through optimal scaling of hip-force profiles

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 133-137).This thesis presents Optimally Scaled Hip-Force Planning (OSHP), a novel approach to controlling the body dynamics of running robots. Controllers based on this approach form the high-level component of a hierarchical control scheme in which they direct lower level controllers, each responsible for coordinating the motion of a single leg. An OSHP controller takes in the state of the runner at the apex of its primary aerial phase and returns desired profiles for the vertical and horizontal forces to be exerted at each hip during the subsequent stride. Controlling the legs so as to match these profiles is left to the lower level leg controllers. The hip force profiles returned by OSHP are scaled variants of nominal force profiles based on biological ground reaction force data. The OSHP controller determines the scaling parameters for these profiles through constrained nonlinear optimization on an approximate model of the runner's body dynamics. Additionally this thesis presents an implementation of an OSHP controller for a simple quadruped model. Evaluation of the controller in simulation shows that even with very simple leg controllers, the OSHP controller can produce bounding and pronking gaits in that model. These gaits emerge as the controller attempts to match particular targets for the runners' states at the apex of their strides. The order in which the feet make contact with ground is not pre-specified. That evaluation also shows that the OSHP controller can compensate for errors introduced by the leg controllers to match given target values for the runners' height, pitch, and pitch rate at the apex of their strides.by Andrés Klee Valenzuela.S.M

Online receding horizon planning of multi-contact locomotion

Legged robots can traverse uneven terrain by using multiple contacts between their limbs and the environment. Nevertheless, to enable reliable operation in the real world, legged robots necessarily require the capability to online re-plan their motions in response to changing conditions, such as environment changes, or state deviations due to external force perturbations. To approach this goal, Receding Horizon Planning (RHP) can be a promising solution. RHP refers to the planning framework that can constantly update the motion plan for immediate execution. To achieve successful RHP, we typically need to consider an extended planning horizon, which consists of an execution horizon that plans the motion to be executed, and a prediction horizon that foresees the future. Although the prediction horizon is never executed, it is important to the success of RHP. This is because the prediction horizon serves as a value function approximation that evaluates the feasibility and the future effort required for accomplishing the given task starting from a chosen robot state. Having such value information can guide the execution horizon toward the states that are beneficial for the future. Nevertheless, computing such multi-contact motions for a legged robot to traverse uneven terrain can be time-consuming, especially when considering a long planning horizon. The computation complexity typically comes from the simultaneous resolution of the following two sub-problems: 1) selecting a gait pattern that specifies the sequence in which the limbs break and make contact with the environment; 2)synthesizing the contact and motion plan that determines the robot state trajectory along with the contact plan, i.e., contact locations and contact timings. The issue of gait pattern selection introduces combinatorial complexity into the planning problem,while the computation of the contact and motion plan brings high-dimensionality and non-convexity due to the consideration of complex non-linear dynamics constraints. To facilitate online RHP of multi-contact motions, in this thesis, we focus on exploring novel methods to address these two sub-problems efficiently. To give more detail, we firstly consider the problem of planning contact and motion plans in an online receding horizon fashion. In this case, we pre-specifying the gait pattern as a priori. Although this helps us to avoid the combinatorial complexity, the resulting planning problem is still high-dimensional and non-convex, which can hinder online computation. To improve the computation speed, we propose to simplify the modeling of the value function approximation that is required for guiding the RHP. This leads to 1) Receding Horizon Planning with Multiple Levels of Model Fidelity, where we compute the prediction horizon with a convex relaxed model; 2) Locally- Guided Receding Horizon Planning—where we propose to learn an oracle to predict local objectives (intermediate goals) for completing a given task, and then we use these local objectives to construct local value functions to guide a short-horizon RHP. We evaluate our methods for planning centroidal trajectories of a humanoid robot walking on moderate slopes as well as large slopes where static stability cannot be maintained.The result of multi-fidelity RHP demonstrates that we can accelerate the computation speed by relaxing the model accuracy in the prediction horizon. However, the relaxation cannot be arbitrary. Furthermore, owing to the shortened planning horizon, we find that locally-guided RHP demonstrates the best computation efficiency (95%-98.6%cycles converge online). This computation advantage enables us to demonstrate online RHP for our real-world humanoid robot Talos walking in dynamic environments that change on-the-fly. To handle the combinatorial complexity that arises from the gait pattern selection issue, we propose the idea of constructing a map from the task specifications to the gait pattern selections for a given environment model and performance objective(cost). We show that for a 2D half-cheetah model and a quadruped robot, a direct mapping between a given task and an optimal gait pattern can be established. We use supervised learning to capture the structure of this map in the form of gait regions.Furthermore, we also find that the trajectories in each gait region are qualitatively similar. We utilize this property to construct a warm-starting trajectory for each gait region, i.e., the mean of the trajectories discovered in each region. We empirically show that these warm-starting trajectories can improve the computation speed of our trajectory optimization problem up to 60 times when compared with random initial guesses. Moreover, we also conduct experimental trials on the ANYmal robot to validate our method