Integrated Planning and Control (IPC) for Mobile Robots
Autonomous navigation in constrained operating spaces is one of the fundamental problems in mobile robotics. Determining how to reach the target point while avoiding obstacles is the planning problem, and moving the robot is a controls problem. On the fundamental level, the robotic system must be capable of deducing the control commands to accomplish the required motion.
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The bounds of the operating space sensed by a 3D robot.
Fundamental aspects for practical deployment
Practical operating scenarios require adaptability to the unknown geometry of the constrained workspaces, accountability for the robot's dimensions, and dealing with disturbances that creep in during run-time to ensure safety.
Critically, sensing and estimating the bounds of safety during run-time is essential for any autonomous agent. The problem becomes more complex in dynamic scenarios when sensed information often becomes obsolete between consecutive sampling instances. Therefore, the requirement of fast planning and control computations becomes inevitable in such settings.
Motion constraints on the minimum admissible radius of curvature of motion and non-holonomy pose inherent challenges in the control of ground mobile robotic systems such as car-like, differential drive, tractor-trailers, etc.
Given an arbitrary obstacle configuration, the IPC Problem seeks a motion plan in the space of the admissible controls (without the explicit requirement of paths/trajectories in the configuration space of the system) of the mobile robotic system such that the induced system's state trajectories converge to the target while remaining confined within the bounds of safety.
Motivation
In recent times, modern techniques in control theory aim to exploit set invariance as a tool for enforcing safety in systems. Control barrier functions (CBFs) and barrier certificates are formal methods available in the literature for the synthesis of safe controllers that guarantee safety through set invariance properties. Given a nominal stabilizing controller, optimization-based techniques are employed to synthesize safe controllers by modifying (minimal) the stabilizing control action based on the safety constraints provided by CBFs. In scenarios where such nominal stabilizers are unavailable, the entire control structure consisting of stability constraints provided by control lyapunov functions and safety constraints provided by barrier functions is posed as a finite horizon online optimization problem to compute control inputs that cater to both stability and safety (often based on the constraints identified during run-time through onboard sensing). Although the control inputs computed as a solution to this optimization problem guarantee stability and safety, solving them in real-time is often challenging as they are computationally intensive owing to the underlying non-convexity in the constraints, non-linearities in system models, and sometimes even due to infeasibility that arise due to the constraints. The associated non-convexities also tend to pose difficulties in finding the global optimizer. Consequently, more often than not the computed solution is sub-optimal. Moreover, computationally tractable solutions for such optimization-based formulations are only achieved through numerical approximations, and linearization (subsequent discretization) of the system models. Therefore, the reliability of such methods is subject to the accuracy of discretization of underlying system models, careful tuning of the parameters such as prediction and control horizons, and more importantly, the available onboard resources to handle online optimizations during real-time.
Research Problem:
Feedback controllers have been the fundamental tools for providing stability and robustness in the face of uncertainties encountered during practical operating scenarios. Such controllers synthesized through lyapunov-based techniques also exhibit closed-form solutions that can readily be used for control computations. Furthermore, set invariance is a natural property of such feedback controllers, and the geometric structure of their associated invariant sets can be explicitly characterized. Since such feedback controllers are synthesized offline, identifying control sequences during run-time becomes computationally light, and planning is directly carried out through the associated invariant sets to guarantee safety. Consequently, a sequence of feedback controllers that induce system trajectories such that they converge to the target while remaining within the bounds of safety is identified during run-time.
In the research problem under focus, we seek to develop such strategies for various applications such as navigation, docking, etc. involving varying classes of 2D/3D non-holonomic mobile robots operating in unknown/previously unmapped environments under the aspects mentioned above. Furthermore, the available research literature that handles the essential aspects as stated earlier is scarce. This motivates the problem from both the research and application perspectives.