Unified Nonlinear Model Predictive Path-Following Control with Collision Avoidance for Robotic Systems

Abstract

Robotic systems operating in constrained environments must often follow prescribed geometric paths while respecting nonlinear dynamics, actuator limits, state constraints, and obstacle-clearance requirements. Conventional trajectory tracking prescribes both path and timing, which can become restrictive when the motion is dynamically infeasible or when obstacle avoidance requires temporary deviation from the prescribed path. This dissertation develops a unified nonlinear Model Predictive Path-Following Control (MPPFC) framework with collision avoidance, in which path following, path progression, dynamics, constraints, and obstacle avoidance are jointly optimized within a single Model Predictive Control (MPC) problem. The central contribution is a complete computational framework that makes the unified collision-aware MPPFC formulation practical by developing analytical collision-constraint derivatives and a tailored primal–dual interior-point solver for the resulting nonlinear control problem. Progression along the prescribed path is optimized online rather than imposed through a fixed time parameterization, allowing adaptation when actuator limits, dynamic constraints, or obstacle-clearance requirements become active. Smooth composite Bezier paths provide analytical path derivatives, while differentiable minimum-distance collision constraints provide analytical gradients and Hessians through closest-point sensitivity analysis and articulated kinematic propagation. The resulting nonlinear optimal-control problem is solved using a second order primal–dual interior-point method tailored to the structured prediction horizon formulation of MPPFC. The solver incorporates analytical derivatives, slack and relaxation variables, barrier terms, scaling, regularization, warm starting, and sparse Newton-system solution. By preserving the stage-wise temporal structure, the method efficiently handles path-following objectives, nonlinear dynamics, constraints, and collision-avoidance inequalities online. The proposed methods are evaluated on two robotic systems: an articulated tractor–trailer navigating around static and dynamic obstacles, and an underactuated planar log-arm robot performing constrained path following. These studies show that adaptive path progression, obstacle avoidance, constraint satisfaction, and feasible control generation can be handled within a unified predictive control framework for nonlinear systems subject to actuator limits, obstacle interactions, changing clearance constraints, and limited actuation, while preserving a computational structure suitable for future real-time embedded implementation.