Trajectory Generation for Mobile Manipulators with Differential Geometry

Abstract

As robotics will play a crucial role in the future of our modern societies, the need for advancements in the field is more pronounced than ever. While robots are already present in industrial settings, they are noticeably absent from dynamic environments. Dynamic environments are characterized by other moving agents, such as humans, varying tasks and high safety requirements. With the aim to deploy robots in such environments, Trajectory Generation (TG) becomes crucial. TG approaches aim to compute sequences of control commands that bring the robot from its current configuration to a desired goal state while avoiding collisions with obstacles and itself. Thus, it is directly placed between task planning, the problem of defining what high level tasks should be executed in which order, and control, the problem of executing motor commands. A good solution to TG must be fast, to cope with changes in the environment, flexible to different goal definitions, and it should promote safety. Most advancements in the field of robotics in TG focus either on manipulators or on mobile robots. However, the combination of both systems seems inevitable for deployment in human-shared environments.

TG for mobile manipulation is usually formulated as an optimization problem of a finite time horizon. This approach is known as Model Predictive Control (MPC) and is widely used in the field of autonomous driving thanks to its feasibility and stability guarantees. In Chapter 4, we present a method to bring MPC to mobile manipulation. The method formulates the TG problem for the entire kinematic chain and relies on Free Space Decomposition (FSD) for collision avoidance. This leads to reasonable control frequencies of 10Hz independent on the amount of collision obstacles in the environment. Importantly, this approach allows for coupled motion of the mobile base and the manipulator. This is beneficial in situations where synchronization of the two subsystems is crucial, such as opening doors or moving obstacles around. Despite these simplifications on the environment representations, computational costs limit the applicability of MPC to mobile manipulation as motion is not considered truly reactive and different components, such as goal attraction and collision avoidance, are not easily separable.

A recent novel approach to receding horizon control is the formulation as a purely geometric problem. Early successes in this direction, including Cartesian Impedance Control (IC) and Artificial Potential Fields (APF), led to the formulation as sets of dynamical systems on smooth manifolds in the configuration space. The framework of Optimization Fabrics (fabrics) unifies such ideas, offers stability guarantees in static environments, and results in highly reactive behavior similar to simple low-level controllers. This framework relies on non-Riemannian geometry to shape a smooth manifold of the configuration space with individual behaviors, such as collision avoidance, joint-limit avoidance, and goal attraction. In Chapter 5, we present a generalization of fabrics to dynamic environments. We refer to the resulting framework as Dynamic Fabrics (DF). The generalization uses time-parameterized manifolds to integrate moving obstacles and time-parameterized reference trajectories. The latter is especially important for long-horizon TG that may exhibit local minima. Importantly, Chapter 5 shows that the dynamic component of DF is required when coping with moving obstacles. As repulsive forces in fabrics are proportional to the approaching speed of obstacle and robot, collision avoidance in a pseudo-static fashion is not sufficient when the robot is moving slowly. Finally, we deploy the general framework of DF to several real-world settings showing the applicability of the framework to mobile manipulation. First, we present a way to integrate non-holonomic constraints into the framework. Despite loosing formal guarantees on convergence, the method is shown to be the natural extension to wheeled mobile robots characterized by non-holonomic constraints. Second, Chapter 6 presents a symbolic implementation of fabrics to achieve higher control frequencies. Symbolic implementations are possible because the framework of fabrics is based on differential equations of second order, for which a closed-form solution exists. For changing environments, obstacles states are then only concretized at runtime. Additionally, we show symbolic hyperparameters can be tuned automatically to achieve expert-level tuning performance. Third, to overcome high requirements on the perception pipeline, Chapter 7 integrates different implicit environment representations into the framework. Using Signed Distance Field (SDF) and FSD for example is widely used in mobile robotics when formulating TG as MPC. We show that the same representations can be used in fabrics while achieving faster solver times. Finally, Chapter 8 deploys a mobile manipulator controlled by fabrics in a supermarket. Dexterous manipulation is programmed using learning-from-demonstration, with fabrics as the underlying encoding. That allows to teach rather than program complicated behaviors while maintaining properties on collision avoidance.

This thesis presents insights into aspects of motion planning, advances the framework of fabrics for TG, and compares it extensively to the more commonly used method of MPC. Through the ideas presented in this thesis, we hope to encourage the usage of geometric properties of robotic systems deployed to human-shared environments. This approach does not only provide reactive TG but also may act as a compact encoding of trajectories for learning-based methods in the future.