A contact-implicit direct trajectory optimization scheme for the study of legged maneuverability

For legged robots to move safely in unpredictable environments, they need to be manoeuvrable, but transient motions such as acceleration, deceleration and turning have been the subject of little research compared to constant-speed gait. They are difficult to study for two reasons: firstly, the way they are executed is highly sensitive to factors such as morphology and traction, and secondly, they can potentially be dangerous, especially when executed rapidly, or from high speeds. These challenges make it an ideal topic for study by simulation, as this allows all variables to be precisely controlled, and puts no human, animal or robotic subjects at risk. Trajectory optimization is a promising method for simulating these manoeuvres, because it allows complete motion trajectories to be generated when neither the input actuation nor the output motion is known. Furthermore, it produces solutions that optimize a given objective, such as minimizing the distance required to stop, or the effort exerted by the actuators throughout the motion. It has consequently become a popular technique for high-level motion planning in robotics, and for studying locomotion in biomechanics. In this dissertation, we present a novel approach to studying motion with trajectory optimization, by viewing it more as “trajectory generation” – a means of generating large quantities of synthetic data that can illuminate the differences between successful and unsuccessful motion strategies when studied in aggregate. One distinctive feature of this approach is the focus on whole-body models, which capture the specific morphology of the subject, rather than the highly-simplified “template” models that are typically used. Another is the use of “contact-implicit” methods, which allow an appropriate footfall sequence to be discovered, rather than requiring that it be defined upfront. Although contact-implicit methods are not novel, they are not widely-used, as they are computationally demanding, and unnecessary when studying comparatively-predictable constant speed locomotion. The second section of this dissertation describes innovations in the formulation of these trajectory optimization problems as nonlinear programming problems (NLPs). This “direct” approach allows these problems to be solved by general-purpose, open-source algorithms, making it accessible to scientists without the specialized applied mathematics knowledge required to solve NLPs. The design of the NLP has a significant impact on the accuracy of the result, the quality of the solution (with respect to the final value of the objective function), and the time required to solve the proble

A Novel Lockable Spring-loaded Prismatic Spine to Support Agile Quadrupedal Locomotion

This paper introduces a way to systematically investigate the effect of compliant prismatic spines in quadrupedal robot locomotion. We develop a novel spring-loaded lockable spine module, together with a new Spinal Compliance-Integrated Quadruped (SCIQ) platform for both empirical and numerical research. Individual spine tests reveal beneficial spinal characteristics like a degressive spring, and validate the efficacy of a proposed compact locking/unlocking mechanism for the spine. Benchmark vertical jumping and landing tests with our robot show comparable jumping performance between the rigid and compliant spines. An observed advantage of the compliant spine module is that it can alleviate more challenging landing conditions by absorbing impact energy and dissipating the remainder via feet slipping through much in cat-like stretching fashion.Comment: To appear in 2023 IEEE IRO

Optimization-based control and planning for highly dynamic legged locomotion in complex environments

Legged animals can dynamically traverse unstructured environments in an elegant and efficient manner, whether it be running down a steep hill or leaping between branches. To harness part of the animal agility to the legged robot would unlock potential applications such as disaster response and planetary exploration. The unique challenge of these tasks is that the robot has to produce highly dynamic maneuvers in complex environments with minimum human guidance. This thesis explores how an optimization-based method can be applied in the control and planning of highly dynamic legged motions to address the locomotion problem in complex environments. Specifically, this work first describes the design synthesis of a small and agile quadrupedal robot \panther. Based on the quadruped platform, we developed a model predictive control (MPC) control framework to realize complex 3D acrobatic motions without resorting to switching among controllers. We present the MPC formulation that directly uses the rotation matrix, which avoids the singularity issue associated with Euler angles. Motion planning algorithms are developed for planar-legged robot traversing challenging terrains. Dynamic trajectories that simultaneously reason about contact, centroidal dynamics, and joint torque limit are obtained by solving mixed-integer convex programs (MICP) without requiring any initial guess from the operator. We further reduce the computational expense of long-horizon planning by leveraging the benefits of both optimization and sampling-based approaches for a simple legged robot. Finally, we present experimental results for each topic on legged robot hardware to validate the proposed method. It is our hope that the results presented in this thesis will eventually enable legged robots to achieve mobility autonomy at the level of biological systems

Optimization-based multi-contact motion planning for legged robots

For legged robots, generating dynamic and versatile motions is essential for interacting with complex and ever-changing environments. So far, robots that routinely operate reliably over rough terrains remains an elusive goal. Yet the primary promise of legged locomotion is to replace humans and animals in performing tedious and menial tasks, without requiring changes in the environment as wheeled robots do. A necessary step towards this goal is to endow robots with capabilities to reason about contacts but this vital skill is currently missing. An important justification for this is that contact phenomena are inherently non-smooth and non-convex. As a result, posing and solving problems involving contacts is non-trivial. Optimization-based motion planning constitutes a powerful paradigm to this end. Consequently, this thesis considers the problem of generating motions in contact-rich situations. Specifically, we introduce several methods that compute dynamic and versatile motion plans from a holistic optimization perspective based on trajectory optimization techniques. The advantage is that the user needs to provide a high-level task description in the form of an objective function only. Subsequently, the methods output a detailed motion plan—that includes contact locations, timings, gait patterns—that optimally achieves the high-level task. Initially, we assume that such a motion plan is available, and we investigate the relevant control problem. The problem is to track a nominal motion plan as close as possible given external disturbances by computing inputs for the robot. Thus, this stage typically follows the motion planning stage. Additionally, this thesis presents methods that do not necessarily require a separate control stage by computing the controller structure automatically. Afterwards, we proceed to the main parts of this thesis. First, assuming a pre-specified contact sequence, we formulate a trajectory optimization method reminiscent of hybrid approaches. Its backbone is a high-accuracy integrator, enabling reliable long-term motion planning while satisfying both translational and rotational dynamics. We utilize it to compute motion plans for a hopper traversing rough terrains—with gaps and obstacles—and performing explosive motions, like a somersault. Subsequently, we provide a discussion on how to extend the method when the contact sequence is unspecified. In the next chapter, we increase the complexity of the problem in many aspects. First, we formulate the problem in joint-level utilizing full dynamics and kinematics models. Second, we assume a contact-implicit perspective, i.e. decisions about contacts are implicitly defined in the problem’s formulation rather than defined as explicit contact modes. As a result, pre-specification of the contact interactions is not required, like the order by which the feet contact the ground for a quadruped robot model and the respective timings. Finally, we extend the classical rigid contact model to surfaces with soft and slippery properties. We quantitatively evaluate our proposed framework by performing comparisons against the rigid model and an alternative contact-implicit framework. Furthermore, we compute motion plans for a high-dimensional quadruped robot in a variety of terrains exhibiting the enhanced properties. In the final study, we extend the classical Differential Dynamic Programming algorithm to handle systems defined by implicit dynamics. While this can be of interest in its own right, our particular application is computing motion plans in contact-rich settings. Compared to the method presented in the previous chapter, this formulation enables experiencing contacts with all body parts in a receding horizon fashion, albeit with limited contact discovery capabilities. We demonstrate the properties of our proposed extension by comparing implicit and explicit models and generating motion plans for a single-legged robot with multiple contacts both for trajectory optimization and receding horizon settings. We conclude this thesis by providing insights and limitations of the proposed methods, and possible future directions that can improve and extend aspects of the presented work

Instantaneous Momentum-Based Control of Floating Base Systems

In the last two decades a growing number of robotic applications such as autonomous drones, wheeled robots and industrial manipulators started to be employed in several human environments. However, these machines often possess limited locomotion and/or manipulation capabilities, thus reducing the number of achievable tasks and increasing the complexity of robot-environment interaction. Augmenting robots locomotion and manipulation abilities is a fundamental research topic, with a view to enhance robots participation in complex tasks involving safe interaction and cooperation with humans. To this purpose, humanoid robots, aerial manipulators and the novel design of flying humanoid robots are among the most promising platforms researchers are studying in the attempt to remove the existing technological barriers. These robots are often modeled as floating base systems, and have lost the assumption -- typical of fixed base robots -- of having one link always attached to the ground. From the robot control side, contact forces regulation revealed to be fundamental for the execution of interaction tasks. Contact forces can be influenced by directly controlling the robot's momentum rate of change, and this fact gives rise to several momentum-based control strategies. Nevertheless, effective design of force and torque controllers still remains a complex challenge. The variability of sensor load during interaction, the inaccuracy of the force/torque sensing technology and the inherent nonlinearities of robot models are only a few complexities impairing efficient robot force control. This research project focuses on the design of balancing and flight controllers for floating base robots interacting with the surrounding environment. More specifically, the research is built upon the state-of-the-art of momentum-based controllers and applied to three robotic platforms: the humanoid robot iCub, the aerial manipulator OTHex and the jet-powered humanoid robot iRonCub. The project enforces the existing literature with both theoretical and experimental results, aimed at achieving high robot performances and improved stability and robustness, in presence of different physical robot-environment interactions