🚶 Escape the Knot: The Yeshwantpur–Mathikere Mobility Nexus

A Physics-Based Pedestrian Accessibility Audit & Simulation Suite

Authors: Aaitijhya Goswami & Prajwal Kagalgomb
Partner Organisation: Bengawalk
Programme: YLAC Mobility Champions 2026

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📖 Overview

This interactive dashboard is a Pedestrian Mobility Audit and Agent-Based Simulation Suite developed to quantify the infrastructural tax imposed on pedestrians at the Yeshwantpur Mobility Knot in Bengaluru. It combines physics-driven modelling with ground-level advocacy to make a data-backed case for the transformation of Yeshwantpur into a "Lighthouse Pilot" for seamless, standards-compliant intermodal pedestrian infrastructure.

By treating the city as a physical system, where broken drains, encroachments, and missing footpaths act as potential energy barriers Φ(x), the commuter's journey becomes analogous to mechanical work done against a spatially varying friction field. Just as the work required to move an object across a rough surface is:

$$W = \int_0^D F(x) dx = \int_0^D \mu(x) mg dx$$

we define the Effective Path Length as the friction-weighted integral over the surveyed corridor of total length D:

$$L_{eff}(\phi) = \int_0^D f(x, \phi) dx$$

where f(x, φ) ∈ [1, 5] is a continuous friction field derived from discrete audit observations, and φ is the commuter persona. In the discretised implementation over N path segments of equal physical length d = D/N:

$$L_{eff}(\phi) \approx d \sum_{i=1}^{N} f_i(\phi)$$

The ratio L_eff / D is the mean friction index of the route. For the Yeshwantpur survey, this evaluates to approximately 4.625, meaning the corridor imposes the equivalent of traversing a path 4.625× its physical length on a frictionless surface. The result is a Time Tax Δτ(φ) (the measurable seconds stolen from each commuter per trip) which, summed across 100,000+ daily users and 250 working days, becomes the headline economic argument for infrastructure intervention.

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🗺️ Campaign Context

Survey Area (March 7–8, 2026): The 900m stretch connecting Yeshwantpur Railway Station to Constitution Circle, the SWR–Metro interchange corridor, and the 0.45 km² Mathikere road network.

Policy Target: Mandate Tender S.U.R.E. Design Standards via DULT's Active Mobility Bill, specifically replacing open box drains with integrated "Pipe and Chamber" systems to create a continuous, accessible walking surface.

Friction Distribution — 900m Yeshwantpur Stretch (Survey Results)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
f = 5  (Systemic Failure)   ████████████████████  79.18%
f = 4  (Physical Barrier)   ███                   11.11%
f = 3  (Obstacle Course)    █                      4.16%
f = 2  (Distracted Walk)    █                      5.55%
f = 1  (Gold Standard)                             Reference
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
  90.3% of the stretch fails Active Mobility Bill standards
  96.0% is fully inaccessible for individuals in wheelchairs

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🚀 The Modules

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1. Spatial Friction Mapper — friction_mapper.py

• Abstract: This module models the survey-audited route as a discretised path, assigning a friction value f ∈ {1, 2, 3, 4, 5} to each geotagged obstacle node based on the Active Mobility Bill rubric. The rubric maps observable infrastructure states to ordinal friction levels, which are then treated as piecewise-constant values over the path segment surrounding each obstacle. For a route partitioned into N segments, the mean friction index is:

$$\bar{f} = \frac{1}{N} \sum_{i=1}^{N} f_i = \frac{L_{eff}}{D}$$

The 900m route is treated as two structurally distinct zones. The 600m Bazaar Street stretch is a continuous f = 5 failure (footpath ends entirely, pedestrians enter vehicular ROW) contributing directly to L_eff:

$$L_{eff}^{600} = 600 \times 5 = 3000 \text{ m}$$

The 300m Constitution Circle stretch has 24 geotagged discrete obstacles: 9 at f = 5, 8 at f = 4, 4 at f = 3, and 3 at f = 2. With segment length d = 300/24 = 12.5 m:

$$L_{eff}^{300} = 12.5 \times \sum_{i=1}^{24} f_i = 12.5 \times (9{\times}5 + 8{\times}4 + 4{\times}3 + 3{\times}2) = 12.5 \times 95 = 1187.5 \text{ m}$$

The total effective path length and mean friction index across the full 900m corridor are therefore:

$$L_{eff} = 3000 + 1187.5 = 4187.5 \text{ m} \qquad \bar{f} = \frac{L_{eff}}{D} = \frac{4187.5}{900} \approx 4.653$$

indicating the route imposes nearly 4.65× the energetic cost of a fully compliant footpath. Nodes are snapped to the nearest OSMnx footpath edge using minimum Haversine distance, and f-values are propagated as edge weights in the NetworkX graph for downstream routing.

The friction rubric encodes the following observable-to-value mapping:

f	Infrastructure State	Speed Impact	Wheelchair Access
1	Continuous, unobstructed 3m+ footpath	v = v₀	Full
2	Minor cracks, unlevelled slabs, low cables	v ≈ 0.85 v₀	Partial — discomfort
3	Broken slabs, rubble, utility excavation	v ≈ 0.5 v₀	Severely restricted
4	Missing drain cover, high kerb, partial blockage	v ≈ 0.25 v₀	Effectively impassable
5	Footpath ends — transformer, encroachment, construction	v → 0 (ROW entry)	Fully impassable

• Applications:

  • Rapid, replicable infrastructure audits at any urban mobility knot in India, using the same friction rubric.
  • Generating court-admissible, geotagged evidence maps for PIL filings on pedestrian rights.
  • Providing a quantitative baseline layer for Transit-Oriented Development (TOD) planning around station interchange zones.

• Key Output: An interactive Folium HTML map with colour-coded pins (f = 2 → green, f = 5 → red), a route polyline overlay for the surveyed corridor, and a static Matplotlib PNG for policy brief annexures.

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2. Agent-Based Time Tax Simulator — agent_sim.py

• Abstract: This module computes the traversal time and Time Tax for four commuter personas across the friction-mapped route. The physical model treats each path segment as imposing a velocity penalty governed by the local friction value. Rather than a simple linear reduction, which underestimates the compounding effect of high-friction segments on vulnerable users, we adopt a power-law friction-velocity relationship:

$$v_{eff}(i, \phi) = \frac{v_0(\phi)}{f_i^{,k(\phi)}}$$

The exponent k(φ) captures persona-specific friction sensitivity: a wheelchair user navigating broken slabs loses speed super-linearly compared to an able-bodied adult, reflecting the physical reality that small obstacles that merely slow one person completely stop another. The traversal time for segment i of length d is then:

$$\tau_i(\phi) = \frac{d}{v_{eff}(i, \phi)} = \frac{d \cdot f_i^{,k(\phi)}}{v_0(\phi)}$$

The total actual traversal time across all N segments is:

$$T_{actual}(\phi) = \sum_{i=1}^{N} \tau_i(\phi) = \frac{d}{v_0(\phi)} \sum_{i=1}^{N} f_i^{,k(\phi)}$$

The ideal traversal time (all segments at f = 1, i.e. a fully compliant S.U.R.E. footpath) is simply:

$$T_{ideal}(\phi) = \frac{D}{v_0(\phi)} = \frac{N \cdot d}{v_0(\phi)}$$

The Time Tax per trip per persona is therefore:

$$\Delta\tau(\phi) = T_{actual}(\phi) - T_{ideal}(\phi) = \frac{d}{v_0(\phi)} \left( \sum_{i=1}^{N} f_i^{,k(\phi)} - N \right)$$

Impassability and detour penalty: When $f_i > f_{max}(\phi)$, the segment is impassable for that persona. The agent is rerouted into the vehicular Right-of-Way (ROW), incurring both a geometric detour of length $δ_i$ (the distance to re-enter the footpath after the blockage) and a safety overhead modelled as a velocity penalty multiplier α = 1.5 for walking in traffic:

$$\tau_i^{ROW}(\phi) = \frac{(d + \delta_i) \cdot \alpha}{v_0(\phi)}$$

Economic aggregation: The aggregate daily Time Tax across M commuters and W working days per year is:

$$\mathcal{T}_{year} = M \cdot W \cdot \bar{\Delta\tau} = M \cdot W \cdot \frac{1}{|\Phi|} \sum_{\phi \in \Phi} \Delta\tau(\phi)$$

where Φ is the set of persona types weighted by their estimated population share. For M = 100,000, W = 250, and the Yeshwantpur friction distribution, this yields an estimated loss of ~170 million person-minutes per year — the headline figure for the DULT brief.

What-if scenario (Lighthouse Pilot): When the top-n friction hotspots are set to f = 1, the reduction in Time Tax is:

$$\Delta\tau_{saved}(n, \phi) = \frac{d}{v_0(\phi)} \sum_{j=1}^{n} \left( f_j^{,k(\phi)} - 1 \right)$$

where nodes are sorted in descending order of f_j^{k(\phi)} to identify the maximum-impact fixes first. This directly drives the Streamlit slider — each increment of n shows the marginal gain from one more hotspot repair.

• Applications:

  • Quantifying the disability-adjusted mobility cost imposed on wheelchair users and the elderly by non-compliant infrastructure.
  • Modelling how targeted fixes at the top-N friction hotspots reduce the aggregate Time Tax, providing a prioritised, low-cost recommendation for BBMP and DULT.
  • Extending the framework to other Indian intermodal hubs (e.g. KSR Bengaluru, Majestic) for city-wide friction benchmarking.

• Commuter Personas (φ):

  Agent	v₀ (m/s)	Sensitivity k	f_max	Estimated Time Tax
  🚶 Able-bodied adult	1.4	0.6	5	Baseline
  👴 Elderly commuter	0.9	0.9	4	+60–80%
  ♿ Wheelchair user	0.8	1.2	3 → detour	+120–180%
  🛵 Delivery partner	1.2	0.75	4	+40–60%

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3. Interactive Digital Twin — streamlit_app.py

• Abstract: The Streamlit dashboard is the public-facing face of the project. A live simulation environment that unifies the friction map, agent simulation, and speculative CAD redesign in one place. Users select a commuter persona, slide through "what-if" hotspot-fix scenarios, and watch the Time Tax recalculate in real time. It is designed for two contexts: as a self-explanatory public exhibit on Bengawalk's channels, and as a live demonstration tool in meetings with DULT and BBMP officials.

• Applications:

  • Communicating the human cost of infrastructure neglect to non-technical civic audiences and journalists through interactive, persona-driven storytelling.
  • Demonstrating the marginal return of fixing specific obstacles (e.g. "Fixing just these 3 drains on Bazaar Street saves 38% of the total daily Time Tax") to make the policy ask concrete and costed.
  • Hosting the speculative CAD redesign as an embedded 3D viewer, allowing stakeholders to orbit, inspect, and annotate the proposed Tender S.U.R.E.-compliant corridor.

• Dashboard Panels:

  • Left sidebar: Persona selector, hotspot-fix slider (N = 1–10), "Run Simulation" trigger
  • Centre: Embedded Folium friction map with live route overlay
  • Right panel: Time Tax bar chart (current vs. fixed), per-agent breakdown, aggregate economic loss metric, embedded 3D CAD viewer

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4. Speculative Redesign — CAD Model — cad_viewer/

• Abstract: A static 3D cross-section of the Yeshwantpur corridor redesigned to Tender S.U.R.E. and Active Mobility Bill standards. Rather than modelling the full 900m route, the model covers a single representative 20–30m segment showing what a compliant stretch looks like: a 3m continuous footpath, flush pipe-and-chamber drainage, underground utility duct, and kerb ramps at each end. It is the "Streets of Hope" visual counterpart to the friction audit; concrete enough to hand to a contractor, simple enough to explain to a policymaker. Authored in Zoo.dev's KCL, exported to glTF via the KittyCAD API, and rendered as a static embed in the Streamlit dashboard.

• Applications:

  • Giving DULT and BBMP reviewers a dimensioned picture of exactly what the Lighthouse Pilot intervention involves — not a concept sketch, but a measurable cross-section.
  • Serving as the "before vs. after" visual for Bengawalk's Instagram and X "Friction Files" posts.
  • Anchoring the policy brief's Lighthouse Proposal with a visual that non-engineers can immediately read.

• Design specification:

  Element	Dimension
  Footpath width	3m clear, per Tender S.U.R.E.
  Drainage	Pipe and chamber, flush with walking surface
  Kerb ramp	1:12 grade at both ends
  Tactile paving	0.6m warning strip at ramp head
  Utility duct	0.5m wide, underground, lid flush
  Vendor setback	1.5m marked zone behind footpath edge

• Workflow:

  yeshwantpur_section.kcl    # KCL cross-section geometry
        ↓  (Zoo KittyCAD API)
  yeshwantpur_section.glb    # exported glTF
        ↓
  streamlit_app.py           # embedded via streamlit-model-viewer
  

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5. Policy Brief Generator — policy_brief.py

• Abstract: This headless script reads the simulation output and renders a submission-ready 2-page PDF using ReportLab. It packages the friction distribution pie chart, per-agent Time Tax bar chart, and an economic extrapolation table built on the aggregate formula:

$$\mathcal{T}_{year} = M \cdot W \cdot \bar{\Delta\tau}(\phi)$$

where M = 100,000 (daily commuters at the Yeshwantpur hub), W = 250 (working days), and Δτ̄(φ) is the persona-averaged Time Tax per trip from the agent simulation. Converting person-minutes to economic value using the Reserve Bank of India's implicit wage rate for informal workers (~₹50/hr), the brief reports an estimated annual productivity loss of ₹14.2 crore attributable solely to the 900m audited stretch. The one-page "Lighthouse Proposal" then uses the what-if delta:

$$\Delta\tau_{saved}(n) = \frac{d}{v_0} \sum_{j=1}^{n} \left( f_j^{,k} - 1 \right)$$

to show that fixing the top 3 hotspots (estimated cost: ₹8–12 lakh for drain covers and slab repair) recovers approximately 38% of the annual Time Tax — a benefit-to-cost ratio exceeding 10:1. This framing is deliberately calibrated to the language of BBMP project approvals, which require both a cost estimate and a quantified beneficiary impact.

• Applications:

  • Direct submission to DULT, BBMP, and the MLA of the Yeshwantpur constituency as a student-led contribution to the Active Mobility Bill discussion.
  • Annexing as supporting evidence in any future PIL on pedestrian infrastructure non-compliance at the Yeshwantpur hub.
  • Reuse as a template for parallel audits at other Bengaluru transit nodes.

• Run headlessly:

  python simulations/policy_brief.py --fixes 3 --output brief.pdf

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🛠️ Tech Stack

Layer	Tools
Core Simulation	NumPy, SciPy — path integration, friction modelling
Geospatial	OSMnx, GeoPandas, NetworkX, Folium, GeoPy — map data, routing, geotagging
Visualisation	Matplotlib, Plotly, Altair — charts, friction maps, time-series
Web App	Streamlit — interactive Digital Twin dashboard
3D / CAD	Zoo.dev / KCL (authoring) → glTF/GLB export via KittyCAD API → streamlit-model-viewer (embedded viewer)
Reporting	ReportLab — policy brief PDF generation
Data	Pandas — field audit data, interview notes, obstacle logs
Language	Python 3.10+

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💻 Installation & Usage

1. Clone the repository:

   git clone https://github.com/AaitijhyaGoswami/escape-the-knot.git
   cd escape-the-knot

2. Install dependencies:

   pip install -r requirements.txt

3. Run the Streamlit app:

   streamlit run streamlit_app.py

4. Run local simulations (no UI):

   python simulations/agent_sim.py
   python simulations/friction_mapper.py

5. Generate the policy brief PDF:

   python simulations/policy_brief.py --fixes 3 --output brief.pdf

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📂 Project Structure

escape-the-knot/
├── data/
│   ├── audit_log.csv                       # Geotagged obstacle data with f-values
│   ├── interview_notes.md                  # Anonymised interview summaries (Kannada + English)
│   ├── personas.yaml                       # Agent config: v₀, k, f_max, label
│   └── route_nodes.geojson                 # Surveyed path as ordered geospatial nodes
├── simulations/
│   ├── friction_mapper.py                  # Spatial friction map generator
│   ├── agent_sim.py                        # Agent-based Time Tax model
│   └── policy_brief.py                     # Economic impact snapshot → PDF
├── cad_viewer/
│   ├── yeshwantpur_section.kcl             # Zoo.dev KCL source — compliant cross-section
│   ├── yeshwantpur_section.glb             # Exported glTF via KittyCAD API
│   └── viewer.py                           # Streamlit component wrapper
├── streamlit_app.py                        # Interactive Digital Twin dashboard
├── requirements.txt
└── README.md

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🗓️ 14-Day Sprint Roadmap

Phase	Days	Deliverable
Data Harvest	1–4	Field audit, geotagged obstacle log, Kannada interviews
Digital Build	5–9	Streamlit app, agent-based sim, KCL model via Zoo.dev, SWOT slide deck
Synthesis & Advocacy	10–14	Policy brief PDF, Bengawalk 'Friction Files', DULT/BBMP submission

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🤝 Stakeholder Ecosystem

• Regulatory: DULT (Active Mobility Bill), BBMP (infrastructure), BTP (enforcement)
• Transit: BMRCL (Metro), South Western Railway, BMTC (bus)
• Community: IISc student body, Mathikere RWAs, Bengawalk collective
• Frontline: Gig-worker unions, delivery platforms (Swiggy, Zomato, Porter)
• Missing Voices: Sanitation workers, elderly pedestrians, persons with disabilities

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🤝 Contributing

Contributions are welcome — especially extensions of the friction rubric to new survey areas, additional commuter personas, or improvements to the CAD model.

1. Fork the project
2. Create your feature branch (git checkout -b feature/NewSurveyZone)
3. Commit your changes (git commit -m 'Add Mathikere extended audit')
4. Push to the branch (git push origin feature/NewSurveyZone)
5. Open a Pull Request

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📜 License

Distributed under the MIT License. See LICENSE for more information.

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Built with ❤️ for Bengaluru's pedestrians...and for the streets that should belong to them.