This thesis investigates the challenges associated with task allocation and motion planning in dynamic and complex environments involving fleets of mobile robots. The primary objective is to coordinate task allocation and trajectory planning in a manner that promotes balanced workload distribution, formulated as the minimization of the maximum operational cost incurred by any individual robot. A hybrid planning framework is proposed in which centralized task allocation and global path planning are performed under static assumptions, while execution-level feasibility is maintained through local trajectory refinement. Task allocation is formulated using a permutation-matrix representation and explored using multiple solution strategies, including deterministic annealing with Potts neurons, stochastic simulated annealing, and heuristic graph-based methods. The cost matrix, derived from global path planners and representing path length and/or traversal time, enables a systematic comparison of these approaches in terms of solution quality, computational complexity, and scalability. The results indicate that deterministic annealing can produce high-quality, balanced task allocations for small- to mediumscale problem instances, while heuristic methods offer improved robustness and computational efficiency in larger or time-critical scenarios. At the motion-planning level, the framework adapts the CHOMP (Covariant Hamiltonian Optimization for Motion Planning) algorithm to account for the kinematic constraints of non-holonomic wheeled mobile robots. Rather than serving as a standalone global planner, the modified CHOMP formulation is used as a local trajectory refinement mechanism, enabling collision avoidance and feasibility preservation during execution. Experimental and simulation results demonstrate that this approach improves trajectory smoothness and feasibility in moderately dynamic environments, while also highlighting limitations related to scalability and sensitivity to initialization. Overall, this thesis presents an integrated task and motion planning framework that emphasizes structured problem formulation and systematic trade-off analysis rather than universal optimality. By explicitly examining the conditions under which different allocation and motion-planning strategies are effective, the work contributes practical insights into multi-robot coordination and supports the informed deployment of autonomous robotic systems in industrial and logistics automation.