Motion Planning for Underactuated Systems through Path Parameterisation

Underactuated systems are becoming an essential field of study within robotics given the rapid advancement and prevalence of legged and flying systems within the modern world. Planning motions that are dynamically feasible for these systems is integral to achieving natural and dynamic movement, however, a great difficulty posed by underactuation is that the space of feasible motions for these systems is strongly constrained by their dynamics. This thesis investigates the viability of extending path-parameterised motion planning to underactuated systems, where algorithms are proposed in two key areas, sample-based and optimisation-based planning. A focus is placed on systems with a single degree of underactuation, where the scalar dynamics revealed under a path parameterisation can be used for efficient kinodynamic querying and dynamic feasibility verification of generated paths. Within a sample-based context, these features are exploited through the development of a path-parameterised RRT algorithm with a state-based steering strategy that accommodates this degree of underactuation. Within the numerical optimisation front, these features are used to develop a path-parameterised trajectory optimisation method with dynamic feasibility detection, enabling the rapid generation of feasible motions with fine dynamical accuracy. This work demonstrates the advantages of these algorithms in relation to existing approaches, highlighting the successes attributed to the exploitation of this class of underactuated system under a path parameterisation

Modeling, analysis and control of robot-object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

International audienceSo-called robot-object Lagrangian systems consist of a class of nonsmooth underactuated complementarity Lagrangian systems, with a specific structure: an "object" and a "robot". Only the robot is actuated. The object dynamics can thus be controlled only through the action of the contact Lagrange multipliers, which represent the interaction forces between the robot and the object. Juggling, walking, running, hopping machines, robotic systems that manipulate objects, tapping, pushing systems, kinematic chains with joint clearance, crawling, climbing robots, some cable-driven manipulators, and some circuits with set-valued nonsmooth components, belong this class. This article aims at presenting their main features, then many application examples which belong to the robot-object class, then reviewing the main tools and control strategies which have been proposed in the Automatic Control and in the Robotics literature. Some comments and open issues conclude the article