Embedded systems are often designed as complex architectures with numerous processing elements. Effectively programming such systems requires parallel programming models e.g task-based or dataflow-based models. With these types of models, the mapping of the abstract application model to the existing hardware architecture plays a decisive role and is usually optimized to achieve an ideal resource footprint or a near-minimal execution time. However, when mapping several independent programs to the same platform, resource conflicts can arise. This can be circumvented by remapping some of the tasks of an application, which in turn affect its timing behavior, possibly leading to constraint violations. In this work we present a novel method to compute mappings that are robust against local task remapping. The underlying method is based on the bio-inspired design centering algorithm of Lp-Adaptation. We evaluate this with several benchmarks on different platforms and show that mappings obtained with our algorithm are indeed robust. In all experiments, our robust mappings tolerated significantly more run-time perturbations without violating constraints than mappings devised with optimization heuristics.