Robot motion can be described in several alternative representations, including
joint configuration or end-effector spaces. These representations are often used for
manipulation or navigation tasks but they are not suitable for tasks that involve
close interaction with the environment. In these scenarios, collisions and relative
poses of the robot and its surroundings create a complex planning space. To deal
with this complexity, we exploit several representations that capture the state of
the interaction, rather than the state of the robot. Borrowing notions of topology invariances
and homotopy classes, we design task spaces based on winding numbers
and writhe for synthesizing winding motion, and electro-static fields for planning
reaching and grasping motion. Our experiments show that these representations
capture the motion, preserving its qualitative properties, while generalising over
finer geometrical detail. Based on the same motivation, we utilise a scale and
rotation invariant representation for locally preserving distances, called interaction
mesh. The interaction mesh allows for transferring motion between robots of
different scales (motion re-targeting), between humans and robots (teleoperation)
and between different environments (motion adaptation). To estimate the state of
the environment we employ real-time sensing techniques utilizing dense stereo
tracking, magnetic tracking sensors and inertia measurements units.
We combine and exploit these representations for synthesis and generalization
of motion in dynamic environments. The benefit of this method is on problems
where direct planning in joint space is extremely hard whereas local optimal control
exploiting topology and metric of these novel representations can efficiently
compute optimal trajectories. We formulate this approach in the framework of
optimal control as an approximate inference problem. This allows for consistent
combination of multiple task spaces (e.g. end-effector, joint space and the abstract
task spaces we investigate in this thesis).
Motion generalization to novel situations and kinematics is similarly performed
by projecting motion from abstract representations to joint configuration space.
This technique, based on operational space control, allows us to adapt the motion
in real time. This process of real-time re-mapping generates robust motion, thus
reducing the amount of re-planning.We have implemented our approach as a part
of an open source project called the Extensible Optimisation library (EXOTica).
This software allows for defining motion synthesis problems by combining task
representations and presenting this problem to various motion planners using a
common interface. Using EXOTica, we perform comparisons between different
representations and different planners to validate that these representations truly
improve the motion planning
