Temporal, spatial, and logical modeling in robotic motion planning and control with uncertainties

Abstract

In traditional factories, robots usually operate known object poses with the help of markers and fixtures. The environments are static and designed for robots. However, as labor shortages and population aging intensify, robots need to work in human-friendly environments or just wild nature. Both of them contain various uncertainties, and three major kinds of uncertainties are vital for robotic motion: (1) environmental uncertainties including kinematics and dynamics with unexpected external disturbances; (2) task uncertainties including various attributes of objects(poses, shape, size, ...); and (3) configuration uncertainties of the robot itself due to nonideal control performance or disabilities. Traditional robotic motion planning and control designed for factory robotics cannot meet these uncertainties (3u: unstructured environments, uncertain tasks, and unperfect configurations). Human motion, however, can adapt to those even with sudden disability or aches of partial body. Therefore, in pursuing similar cerebellar intelligence of robots under such uncertainties, we identified three exact issues: (a) "How can motion plan best be parameterized to adapt for uncertainty?", (b)"What state representation is best for uncertain object-centric operations?", (c)"How can complex task criteria be met with an optimal process?". To solve such problems, our research is carried out in the "action level" with discrete but numerical logics, and the"motion level" with continuous spatial-temporal relations.

In the motion level, two novel motion planning and control paradigms are established based on two fundamental changes: (i) motion Reference: from "time-based" to "perceptive-based"; and (ii) state Space: from "vector space" to "non-vector space (NVS)". By combining (i), and (ii), the optimization in NVS for an object-centric complex task can be intuitively accomplished by NVS models of the tool, task criteria, and dynamics. The perceptive reference tube optimizer is formulated for NVS spatial and temporal motion planning respectively. The framework itself is fully mathematically analytical and the control stability is proven by Lyapunov theory.

At the action level, the Finite Sub-task Machine (FSM) is proposed for a complex task with many sub-tasks connected with logic relationships such as "AND", "OR", "NOT". Extended tropical algebra is introduced to convert such logical relationships into operators in the sub-task triggering of FSM. More importantly, the multi-modal (position, force, tactility) perceptive motion references from the motion level are also integrated into the sub-task triggering of FSM, enabling the action level FSM to coordinately solve hybrid (continuous, discrete) and multi-modal (position, force) uncertainties. Meanwhile, the set-covering planner solves the spatial full-coverage problem at the action level by selecting as few viewpoints as possible, further enhancing the flexibility and efficiency of the planned perceptive path in NVS.

All the algorithms are implemented on two advanced mobile robots (a full-size humanoid robot, and an indoor mobile manipulator) in various practical tasks such as walking on stairs and doing outdoors ground inspection or indoor object disinfection. Compared with other traditional and popular methods, our approach handles uncertainties effectively and efficiently. Future work should enable robots to learn world models both from and for physical manipulations in a life-long term, just like humans do.