{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H6GDM5OUTNAXRRA6RGIQ6NMFTJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"56cd39523e1280539693c9fb88304b201aebd302a721a506278ac2d3b59bdf37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-26T11:52:02Z","title_canon_sha256":"5f435acdcbdb47311565f7a0978ed9c14ad4bb2258f61b7e2175fc46ddc4c72b"},"schema_version":"1.0","source":{"id":"1806.09929","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09929","created_at":"2026-05-18T00:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09929v1","created_at":"2026-05-18T00:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09929","created_at":"2026-05-18T00:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"H6GDM5OUTNAX","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H6GDM5OUTNAXRRA6","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H6GDM5OU","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:92323e537958c51b42d12d8359e195a146445ee9730205cbcd0975e6829b4c43","target":"graph","created_at":"2026-05-18T00:12:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we formulate a novel trajectory optimization scheme that takes into consideration the state uncertainty of the robot and obstacle into its collision avoidance routine. The collision avoidance under uncertainty is modeled here as an overlap between two distributions that represent the state of the robot and obstacle respectively. We adopt the minmax procedure to characterize the area of overlap between two Gaussian distributions, and compare it with the method of Bhattacharyya distance. We provide closed form expressions that can characterize the overlap as a function of control.","authors_text":"Akash Garg, Bharath Gopalakrishnan, Dhaivat Bhatt, K. Madhava Krishna","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-26T11:52:02Z","title":"Chance Constraints Integrated MPC Navigation in Uncertainty amongst Dynamic Obstacles: An overlap of Gaussians approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09929","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4888b1b8b1a69ab1aa4105bc1a5f58f87e7cf0f5358520954303b70298b78a34","target":"record","created_at":"2026-05-18T00:12:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"56cd39523e1280539693c9fb88304b201aebd302a721a506278ac2d3b59bdf37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-26T11:52:02Z","title_canon_sha256":"5f435acdcbdb47311565f7a0978ed9c14ad4bb2258f61b7e2175fc46ddc4c72b"},"schema_version":"1.0","source":{"id":"1806.09929","kind":"arxiv","version":1}},"canonical_sha256":"3f8c3675d49b4178c41e89910f35859a64f43ae4e4277cad8c048f23fb1fec2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f8c3675d49b4178c41e89910f35859a64f43ae4e4277cad8c048f23fb1fec2e","first_computed_at":"2026-05-18T00:12:22.805021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:22.805021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pWCNzpQsVvXrndLgKTdeRjtHqfhRSybcO1H4OciK5Uoa3rfFq10XjpJnO0cHhSh65wkY4Vuzv5cNjNuHfiehCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:22.805734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.09929","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4888b1b8b1a69ab1aa4105bc1a5f58f87e7cf0f5358520954303b70298b78a34","sha256:92323e537958c51b42d12d8359e195a146445ee9730205cbcd0975e6829b4c43"],"state_sha256":"ac18e326a510a53e63391a3ff68cdfd1e78cc32e053b021451b9890532191676"}