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As robots move from the laboratory into the real world, motion planning will need to account for model uncertainty and risk. For robot motions involving intermittent contact, planning for uncertainty in contact is especially important, as failure to successfully make and maintain contact can be catastrophic. Here, we model uncertainty in terrain geometry and friction characteristics, and combine a risk-sensitive objective with chance constraints to provide a trade-off between robustness to uncertainty and constraint satisfaction with an arbitrarily high feasibility guarantee. We evaluate our approach in two simple examples: a push-block system for benchmarking and a single-legged hopper. We demonstrate that chance constraints alone produce trajectories similar to those produced using strict complementarity constraints; however, when equipped with a robust objective, we show the chance constraints can mediate a trade-off between robustness to uncertainty and strict constraint satisfaction. Thus, our study may represent an important step towards reasoning about contact uncertainty in motion planning.
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Chance-constrained multi-stage stochastic energy system expansion planning with demand satisfaction flexibility
A classic multi-period stochastic energy system expansion planning (ESEP) model aims to address demand uncertainty by requiring immediate demand satisfaction for all scenarios. However, this approach may result in an expensive system that deviates from the planner’s long-term goals, especially when facing unexpectedly high demand scenarios. To address this issue, we propose a chance-constrained stochastic multi-stage ESEP model that allows for a portion of demand to remain unmet in specific periods while still ensuring complete demand satisfaction during most of the planning horizon, including the final period. This approach provides more time flexibility to build infrastructure and assess needs, ultimately reducing costs and allowing for a broader view of infrastructure planning options. To solve the chance-constrained stochastic model, we introduce a binary- search-based progressive hedging algorithm heuristic, which is particularly useful for large-scale models. We demonstrate the effectiveness and benefits of implementing the chance-constrained model through a case study of Rwanda using real-world data.
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- Award ID(s):
- 2330437
- PAR ID:
- 10625232
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- International Journal of Electrical Power & Energy Systems
- Volume:
- 155
- Issue:
- PA
- ISSN:
- 0142-0615
- Page Range / eLocation ID:
- 109499
- Subject(s) / Keyword(s):
- Energy system expansion planning (ESEP) Multi-stage stochastic optimization Power deficit flexibility Chance constraints Progressive hedging algorithm (PHA) Sub-Saharan Africa
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.ijepes.2023.109499
