Pattern Generation for Rough Terrain Locomotion with Quadrupedal Robots:Morphed Oscillators & Sensory Feedback

Animals are able to locomote on rough terrain without any apparent difficulty, but this does not mean that the locomotor system is simple. The locomotor system is actually a complex multi-input multi-output closed-loop control system. This thesis is dedicated to the design of controllers for rough terrain locomotion, for animal-like quadrupedal robots. We choose the problem of blind rough terrain locomotion as the target of experiments. Blind rough terrain locomotion requires continuous and momentary corrections of leg movements and body posture, and provides a proper testbed to observe the interaction of different mod- ules involved in locomotion control. As for the specific case of this thesis, we have to design rough terrain locomotion controllers that do not depend on the torque-control capability, have limited sensing, and have to be computationally light, all due to the properties of the robotics platform that we use. We propose that a robust locomotion controller, taking into account the aforementioned constraints, is constructed from at least three modules: 1) pattern generators providing the nominal patterns of locomotion; 2) A posture controller continuously adjusting the attitude of the body and keeping the robot upright; and 3) quick reflexes to react to unwanted momentary events like stumbling or an external force impulse. We introduce the framework of morphed oscillators to systematize the design of pattern gen- erators realized as coupled nonlinear oscillators. Morphed oscillators are nonlinear oscillators that can encode arbitrary limit cycle shapes and simultaneously have infinitely large basins of attraction. More importantly, they provide dynamical systems that can assume the role of feedforward locomotion controllers known as Central Pattern Generators (CPGs), and accept discontinuous sensory feedback without the risk of producing discontinuous output. On top of the CPG module, we add a kinematic model-based posture controller inspired by virtual model control (VMC), to control the body attitude. Virtual model control produces forces, and through the application of the Jacobian transpose method, generates torques which are added to the CPG torques. However, because our robots do not have a torque- control capability, we adapt the posture controller by producing task-space velocities instead of forces, thus generating joint-space velocity feedback signals. Since the CPG model used for locomotion generates joint velocities and accepts feedback without the fear of instability or discontinuity, the posture control feedback is easily integrated into the CPG dynamics. More- over, we introduce feedback signals for adjusting the posture by shifting the trunk positions, which directly update the limit cycle shape of the morphed oscillator nodes of the CPG. Reflexes are added, with minimal complexity, to react to momentary events. We implement simple impulse-based feedback mechanisms inspired by animals and successful rough terrain robots to 1) flex the leg if the robot is stumbling (stumbling correction reflex); 2) extend the leg if an expected contact is missing (leg extension reflex); or 3) initiate a lateral stepping sequence in response to a lateral external perturbation. CPG, posture controller, and reflexes are put together in a modular control architecture alongside additional modules that estimate inclination, control speed and direction, maintain timing of feedback signals, etc. [...

A Closed-Loop Optimal Control Approach for Online Control of A Planar Monopod Hopper

In this paper we present a closed-loop optimal control approach for the online control of a legged robot locomotion, particularly the hopping of a simulated monoped robot. Modeling is done based on the spring loaded inverted pendulum (SLIP) model suggested as the animal and human running gait template. The key idea is to efficiently inject energy to the system so that the monoped can track the desired apex height and forward velocity. The state of the system is observed in the Poincare section at the apex point and the corresponding discrete dynamics is formulated by using available analytical solutions. The goal is then to synthesize an optimal control law which can bring the apex state at any step to the desired state at the next step. We show the controller performance in providing fast and accurate response in the presence of noise and through different scenarios while minimizing the control effort

Kinematic primitives for walking and trotting gaits of a quadruped robot with compliant legs

In this work we research the role of body dynamics in the complexity of kinematic patterns in a quadruped robot with compliant legs. Two gait patterns, lateral sequence walk and trot, along with leg length control patterns of different complexity were implemented in a modular, feed-forward locomotion controller. The controller was tested on a small, quadruped robot with compliant, segmented leg design, and led to self-stable and self-stabilizing robot locomotion. In-air stepping and on-ground locomotion leg kinematics were recorded, and the number and shapes of motion primitives accounting for 95% of the variance of kinematic leg data were extracted. This revealed that kinematic patterns resulting from feed-forward control had a lower complexity (in-air stepping, 2 to 3 primitives) than kinematic patterns from on-ground locomotion (4 primitives), although both experiments applied identical motor patterns. The complexity of on-ground kinematic patterns had increased, through ground contact and mechanical entrainment. The complexity of observed kinematic on-ground data matches those reported from level-ground locomotion data of legged animals. Results indicate that a very low complexity of modular, rhythmic, feed-forward motor control is sufficient for level-ground locomotion in combination with passive compliant legged hardware

Data-driven extraction of drive functions for legged locomotion: A study on Cheetah-cub robot

The process of finding working gaits for legged robots always, to different extents, includes manual tuning, systematic search, or optimization of control parameters. This process populates a dataset of control parameter vectors and respective robot behavior factors, like forward speed. The dataset obtained from a tuning process can include many gaits which share a similar performance in one behavior factor, e.g. speed, but differ in the control parameter vectors used. Our question here is, using the tuning dataset, how a continuous drive function can be calculated which takes the desired behavior, e.g. speed, and maps that to a control parameter vector. If this question is answered properly, then the robot operator (or a higher level controller) will have a single control knob to continuously change the desired behavior factor

Trot Gait Locomotion of A Cat Sized Quadruped Robot

We are proposing and testing two model-free approaches for locomotion control of a light-weight, compliant, quadruped robot: open loop central pattern generators (CPG), and open and closed- loop dynamical movement primitives (DMP). We are presenting two different knee joint controllers, based on the hypothesis that the passive- compliant leg design might require less control effort for the knee joint control. CPG-control parameters are optimized applying extensive optimization runs using PSO, resulting trot gaits are evaluated for speed and robustness. One derived gait is selected as learning input for a gait controller based on DMP. We design the DMP-based trot gait controller both for open and closed-loop control. For the latter we are feeding back gyroscope and touch sensor signals to modulate the core phase pattern. Found CPG based trot gaits are up to 90cm/sec fast (more than 3 BL/sec). The joint controller assisting the passive compliant knee joint shows gaits with higher speed, and larger hip amplitude. Closed- loop DMP based gaits let the robot handle frontal and sideways slopes, step-downs, and random pushes to the robot’s COM more robustly

Robot Trotting with Segmented Legs in Simulation and Hardware.

This research is focusing on the implementation, testing, and analysis of quadrupedal, bio-inspired robot locomotion. Our tool of research is a light-weight, quadruped robot of the size of a house cat, both in simulation and hardware. We are currently following the idea of testing bio-inspired blue-prints such as leg-segmentation, directional leg compliance (bio-mechanical), and central pattern generators (bioinspired neuro-control) for their feasibility, and advantages against more traditional, engineered solutions. Clearly, our first goal would be to reach a same level of performance as animals, e.g. in terms of speed, cost of transport, or versatility. Much research has been done on bio-mechanical and neuro-physiological research on legged vertebrates. Hence, data is available for animal locomotion such as gait patterns, speed, cost of transport, duty factor, joint angles, torque patterns, body angles, and ground reaction force (GRF) data. While this data allows one to study a subset of locomotion characteristics, it often lacks an intuitive way to compare animals of different species, or as for us, quadruped robots. We started applying the collision angle analysis (Lee, Bertram, et al. 2011) for trot gait, based on qualitative and quantitative results from goats and dogs (taken from (ibid.)), and experimental recordings of our robot’s center of mass (COM) and GRF