Dynamics and Control of Nonholonomic Systems with Internal Degrees of Freedom

Nonholonomic systems model many robots as well as animals and other systems. Although such systems have been studied extensively over the last century, much work still remains to be done on their dynamics and control. Many techniques have been developed for controlling kinematic nonholonomic systems or simplified dynamic versions, however control of high dimensional, underactuated nonholonomic systems remains to be addressed. This dissertation helps fill this gap by developing a control algorithm that can be applied to systems with three or more configuration variables and just one input. We also analyze the dynamic effects of passive degrees of freedom and elastic potentials which are commonly observed in such systems showing that the addition of a passive degree of freedom can even be used to improve the locomotion characteristics of a system. Such elastic potentials can be present due to compliant mechanisms or origami, both of which can exhibit bistability and many other properties that can be useful in the design of robots

Proprioceptive Invariant Robot State Estimation

This paper reports on developing a real-time invariant proprioceptive robot state estimation framework called DRIFT. A didactic introduction to invariant Kalman filtering is provided to make this cutting-edge symmetry-preserving approach accessible to a broader range of robotics applications. Furthermore, this work dives into the development of a proprioceptive state estimation framework for dead reckoning that only consumes data from an onboard inertial measurement unit and kinematics of the robot, with two optional modules, a contact estimator and a gyro filter for low-cost robots, enabling a significant capability on a variety of robotics platforms to track the robot's state over long trajectories in the absence of perceptual data. Extensive real-world experiments using a legged robot, an indoor wheeled robot, a field robot, and a full-size vehicle, as well as simulation results with a marine robot, are provided to understand the limits of DRIFT

Modeling and adaptive tracking for stochastic nonholonomic constrained mechanical systems

This paper is devoted to the problem of modeling and trajectory tracking for stochastic nonholonomic dynamic systems in the presence of unknown parameters. Prior to tracking controller design, the rigorous derivation of stochastic nonholonomic dynamic model is given. By reasonably introducing so-called internal state vector, a reduced dynamic model, which is suitable for control design, is proposed. Based on the backstepping technique in vector form, an adaptive tracking controller is then derived, guaranteeing that the mean square of the tracking error converges to an arbitrarily small neighborhood of zero by tuning design parameters. The efficiency of the controller is demonstrated by a mechanics system: a vertical mobile wheel in random vibration environment

The Mechanics and Control of Undulatory Robotic Locomotion

In this dissertation, we examine a formulation of problems of undulatory robotic locomotion within the context of mechanical systems with nonholonomic constraints and symmetries. Using tools from geometric mechanics, we study the underlying structure found in general problems of locomotion. In doing so, we decompose locomotion into two basic components: internal shape changes and net changes in position and orientation. This decomposition has a natural mathematical interpretation in which the relationship between shape changes and locomotion can be described using a connection on a trivial principal fiber bundle. We begin by reviewing the processes of Lagrangian reduction and reconstruction for unconstrained mechanical systems with Lie group symmetries, and present new formulations of this process which are easily adapted to accommodate external constraints. Additionally, important physical quantities such as the mechanical connection and reduced mass-inertia matrix can be trivially determined using this formulation. The presence of symmetries then allows us to reduce the necessary calculations to simple matrix manipulations. The addition of constraints significantly complicates the reduction process; however, we show that for invariant constraints, a meaningful connection can be synthesized by defining a generalized momentum representing the momentum of the system in directions allowed by the constraints. We then prove that the generalized momentum and its governing equation possess certain invariances which allows for a reduction process similar to that found in the unconstrained case. The form of the reduced equations highlights the synthesized connection and the matrix quantities used to calculate these equations. The use of connections naturally leads to methods for testing controllability and aids in developing intuition regarding the generation of various locomotive gaits. We present accessibility and controllability tests based on taking derivatives of the connection, and relate these tests to taking Lie brackets of the input vector fields. The theory is illustrated using several examples, in particular the examples of the snakeboard and Hirose snake robot. We interpret each of these examples in light of the theory developed in this thesis, and examine the generation of locomotive gaits using sinusoidal inputs and their relationship to the controllability tests based on Lie brackets

Cooperative Control of Multiple Wheeled Mobile Robots: Normal and Faulty Situations

Recently, cooperative control of multiple unmanned vehicles has attracted a great deal of attention from scientific, industrial, and military aspects. Groups of unmanned ground, aerial, or marine vehicles working cooperatively lead to many advantages in a variety of applications such as: surveillance, search and exploration, cooperative reconnaissance, environmental monitoring, and cooperative manipulation, respectively. During mission execution, unmanned systems should travel autonomously between different locations, maintain a pre-defined formation shape, avoid collisions of obstacles and also other team members, and accommodate occurred faults and mitigate their negative effect on mission execution. The main objectives of this dissertation are to design novel algorithms for single wheeled mobile robots (WMRs) trajectory tracking, cooperative control and obstacle avoidance of WMRs in fault-free situations. In addition, novel algorithms are developed for fault-tolerant cooperative control (FTCC) with integration of fault detection and diagnosis (FDD) scheme. In normal/fault-free cases, an integrated approach combining input-output feedback linearization and distributed model predictive control (MPC) techniques is designed and implemented on a team of WMRs to accomplish the trajectory tracking as well as the cooperative task. An obstacle avoidance algorithm based on mechanical impedance principle is proposed to avoid potential collisions of surrounding obstacles. Moreover, the proposed control algorithm is implemented to a team of WMRs for pairing with a team of unmanned aerial vehicles (UAVs) for forest monitoring and fire detection applications. When actuator faults occur in one of the robots, two cases are explicitly considered: i) if the faulty robot cannot complete its assigned task due to a severe fault, then the faulty robot has to get out from the formation mission, and an FTCC strategy is designed such that the tasks of the WMRs team are re-assigned to the remaining healthy robots to complete the mission with graceful performance degradation. Two methods are used to investigate this case: the Graph Theory, and formulating the FTCC problem as an optimal assignment problem; and ii) if the faulty robot can continue the mission with degraded performance, then the other team members reconfigure the controllers considering the capability of the faulty robot. Thus, the FTCC strategy is designed to re-coordinate the motion of each robot in the team. Within the proposed scheme, an FDD unit using a two-stage Kalman filter (TSKF) to detect and diagnose actuator faults is presented. In case of using any other nonlinear controller in fault-free case rather than MPC, and in case of severe fault occurrence, another FTCC strategy is presented. First, the new reconfiguration is formulated by an optimal assignment problem where each healthy WMR is assigned to a unique place. Second, the new formation can be reconfigured, while the objective is to minimize the time to achieve the new formation within the constraints of the WMRs' dynamics and collision avoidance. A hybrid approach of control parametrization and time discretization (CPTD) and particle swarm optimization (PSO) is proposed to address this problem. Since PSO cannot solve the continuous control inputs, CPTD is adopted to provide an approximate piecewise linearization of the control inputs. Therefore, PSO can be adopted to find the global optimum solution. In all cases, formation operation of the robot team is based on a leader-follower approach, whilst the control algorithm is implemented in a distributed manner. The results of the numerical simulations and real experiments demonstrate the effectiveness of the proposed algorithms in various scenarios